Advance management accounting 4th edition by parag gupta

To my family, who always stood beside me in every phase of my life Love You! Special thanks to my friends, students, teachers & my competitors This book mightn’t have been completed without them Preface to Forth Edition I feel a great sense of pride and enthusiasm in presenting forth edition of my book This book has primarily been written with the aim of meeting the needs and interest of C.A final students Every topic has been dealt precisely and to the point in a simple and understandable language Things have been explained with proper reasoning, wherever possible A good number of practical problems have been provided to understand the theoretical aspect Many new exercises from have been introduced with hints for all difficult exercises The book covers around past While 25 year questions of CA, CWA & CIMA examination till carrying out changes, the general approach to the subject, with an inclusion of a variety of practical problems, and the lucidity of presentation of the subject matter of the previous edition have been retained and an endeavor has been made to give a lot more content to the user-both students and instructors I have deliberately kept this book in question bank format, to help students in solving the problem on their own This helps in gaining confidence Solutions of this book are separately provided While making this book I have tried to cover full new course syllabus & have inserted both new course syllabus & old syllabus, to make aware about the differences between syllabuses Human efforts are not perfect In spite of my best efforts, I am aware of possible errors and omissions that escaped my notice I shall, therefore, be extremely thankful to the learned ones who will extend their cooperation by sending their valuable criticism, suggestions and observations for further improvement of the book I am reachable at paraggupta_ca@yahoo.co.in Dec.’ 2010 CA Parag Gupta   No part of this book may be reproduced or utilized in any form or by  any means  electronic or mechanical including photocopying  recording  or by any information storage and retrieval system  without permission  in writing from author               For any  Costing   O R  related query  you may call me during 9:00 p.m 11:00 p.m.       or mail me at  paraggupta ca yahoo co in      For registration enquiry  any other query  etc  call                          For solutions of Costing  join world s largest free consultancy group of  CA Final students   http groups yahoo com group costingbyparaggupta              Price  Rs                       This book is meant for educational   learning purposes  The author of the book has have taken all responsible care to ensure that the contents of the book do not violate  any existing copyright or other intellectual property rights of any person in any manner whatsoever  In the even the author has have been unable to track any source  and if any copyright has been inadvertently infringed  please notify the author in writing for corrective action   Syllabus - New Course Paper 5: Advanced Management Accounting (One paper – Three hours – 100 marks) Level of Knowledge: Advanced knowledge Objective: To apply various management accounting techniques to all types of organizations for planning, decision making and control purposes in practical situations To develop ability to apply quantitative techniques to business problems Cost Management (a) Developments in the business environment; just in time; manufacturing resources planning; (MRP); automated manufacturing; synchronous manufacturing and back flush systems to reflect the importance of accurate bills of material and routings; world class manufacturing; total quality management (b) Activity based approaches to management and cost analysis (c) Analysis of common costs in manufacturing and service industry (d) Techniques for profit improvement, cost reduction, and value analysis (e) Throughput accounting (f) Target costing; cost ascertainment and pricing of products and services (g) Life cycle costing (h Shut down and divestment Cost Volume Profit Analysis (a) Relevant cost (b) Product sales pricing and mix (c) Limiting factors (d) Multiple scarce resource problems (e) Decisions about alternatives such as make or buy, selection of products, etc Pricing Decisions (a) Pricing of a finished product (b) Theory of price (c) Pricing policy (d) Principles of product pricing (e) New product pricing (f) Pricing strategies (g) Pricing of services (h) Pareto analysis Budgets and Budgetary Control The budget manual, Preparation and monitoring procedures, Budget variances, Flexible budgets, Preparation of functional budget for operating and non-operating functions, Cash budgets, Capital expenditure budget, Master budget, Principal budget factors Standard Costing and Variance Analysis Types of standards and sources of standard cost information; evolution of standards, continuousimprovement; keeping standards meaningful and relevant; variance analysis; disposal of variances (a) Investigation and interpretation of variances and their inter relationship (b) Behavioural considerations Transfer pricing (a) Objectives of transfer pricing (b) Methods of transfer pricing (c) Conflict between a division and a company (d) Multi-national transfer pricing Cost Management in Service Sector Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Uniform Costing and Inter firm comparison Profitability analysis - Product wise / segment wise / customer wise 10 Financial Decision Modeling (a) Linear Programming (b) Network analysis - PERT/CPM, resource allocation and resource leveling (c) Transportation problems (d) Assignment problems (e) Simulation (f) Learning Curve Theory (g) Time series forecasting (h) Sampling and test of hypothesis Important things to be noted: Marginal Costing (incld Marginal v/s Absorption) has been deleted from New Course, although students are expected to comprehensive knowledge about applicability of CVP analysis {As per Mr R Devrajan (Last Director-Board of Studies), since Syllabus of New Course has specifically deleted Marginal costing, there is no need to issue any specific notification in this regards For any clarification, students may compare both new & old course syllabuses} Topics newly introduced have been written in “Times New Roman” Font & are underlined It is advisable to students to read topics like “Balance Scorecard’ for their examination (although they have been specially deleted from New course syllabus), because ICAI is still asking questions from these topics in New course examinations Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Syllabus - Old Course Paper : Cost Management (One paper – Three hours – 100 marks) Level of Knowledge: Expert Knowledge Objectives: To gain expert knowledge of: a) use of costing data for decision-making and control, and b) emerging modern cost management concepts Contents: Cost concepts in decision-making; Relevant cost, Differential cost, Incremental cost and Opportunity cost Objectives of a Costing System; Inventory valuation; Creation of a Database for operational control; Provision of data for Decision-Making Marginal Costing; Distinction between Marginal Costing and Absorption Costing; Break-even Analysis, Cost-Volume-Profit Analysis Various decision-making problems Standard Costing and Variance Analysis Pricing strategies: Pareto Analysis Target costing, Life Cycle Costing Costing of service sector Just-in-time approach, Material Requirement Planning, Enterprise Resource Planning, Total Quality Management and Theory of constraints Activity-Based Cost Management, Bench Marking; Balanced Score Card and Value-Chain Analysis 10 Budgetary Control; Flexible Budgets; Performance budgets; Zero-based budgets 11 Measurement of Divisional profitability pricing decisions including transfer pricing 12 Quantitative techniques for cost management, Linear Programming, PERT/CPM, Transportation problems, Assignment problems, Simulation, Learning Curve Theory Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Question Papers: New Course-Nov.’10 Old Course-Nov.’10 Pages i - iv v-x Chapters: Cost Accounting & Management: CVP Analysis Activity-based costing management Target Costing, Value Chain analysis & Life Cycle Costing Service Sector Standard Costing & Variance Analysis: (i) Variance Analysis (ii) Investigation of Variance (iii) Balance Scorecard Budget & Budgetary Control: (i) Key Factor & Product Mix Decision (ii) TOC, Throughput A/cing & Synchronous Manufacturing (iii) Budgetary Control Transfer Pricing Decision Making: (i) Relevant Costing (ii) Make or Buy (iii) Subcontracting (iv) Export Pricing (v) Shut Down Point & Divestment Strategy (vi) Inventory Decision (vii) Miscellaneous (e.g Joint Cost, D.C.F, etc.) Miscellaneous Theory Chapters: (i) Total Quality Management (TQM) (ii) Pricing Decisions & Pareto Analysis (iii) Benchmarking (iv) JIT & Backflushing (v) MRP I, MRP II & ERP (vi) Computer Aided Manufacturing & Business Process Re-engineering - 17 16 - 33 34 - 59 60 - 72 73 - 114 115 - 117 117 - 122 123 - 131 131 - 135 135 - 153 154 - 181 182 - 206 206 - 213 214 - 216 216 - 217 217 - 221 221 - 223 223 - 233 234 - 245 246 - 254 255 - 257 258 - 265 265 - 268 268 - 268 (vii) Uniform Costing, Inter-firm Comparision & D.P.P Operations Research: 10 Linear Programming Problems 11 The Transportation Problem 12 The Assignment Problem 13 Network Analysis-PERT/CPM 14 Simulation 15 Learning Curve Theory 16 Time Series Analysis & Forecasting 17 Sampling and Test of Hypothesis Tables: Normal Table Student’s t Distribution Chi-Square Distribution F Table for alpha = 0.10 F Table for alpha = 0.05 Log Table Antilog Table 269 - 276 277 - 294 295 - 306 307 - 314 315 - 335 336 - 343 344 - 351 352 - 365 366 - 383 a b c d e f h Sampling & Test of Hypothesis - 378 - [Ans.: t = -2.084 ( x M  x E = -Rs.395), t L = -2.467 (( x M  x E ) L = -Rs.467.59), so not reject H o The data not support the commissioner’s speculation.] Testing Differences between Means with Dependent (or paired) Samples Question 43: The data below are a random sample of nine firms chosen from the “Digest of Earning Reports”, in The Wall Street Journal on Feb 2008: (a) Find the mean change in earnings per share between 2007 & 2008 (b) Find the standard deviation of the change and the standard error of the mean (c) Were average earnings per share different in 2007 & 2008? Test at  = 0.02 Firm 2007 earnings per share 2008 earnings per share 1.38 2.48 1.26 1.50 3.64 4.59 3.50 3.06 2.47 2.11 3.21 2.80 1.05 1.59 1.98 0.92 2.72 0.47 [Ans.: t= -0.5428 ( x = -0.19), tCRIT  2.896( xCRIT  1.01) so not reject H o ] Question 44: Nine computer-components dealers in major metropolitan areas were asked for their prices on two similar dot-matrix printers with standard widths and near-letter-quality fonts The results of this survey are given below At  = 0.05, is it reasonable to assert that, on average, the Apson printer is less expensive than HP Printer? Dealer Apson (Rs.) 350 419 385 360 405 395 389 409 375 HP (Rs.) 370 425 369 375 389 385 395 425 400 [Ans.: t = 0.981 ( x = 5.11), tU  1.80( xU  9.69) so not reject H o Apson is not significantly less expensive] Question 45: The sales data of an item in six shops before and after a special promotional campaign are as under: Shops A B C D E F Before Campaign 53 28 31 48 50 42 After Campaign 58 29 30 55 56 45 Can the compaign be judged to be a success? Test at 5% level of significance using t-test (RTP-Nov/08) [Ans.: t = -2.782, tL  2.015 so reject H o ] Question 46: Divya is a production supervisor on the disk-drive assembly line at XY Ltd XY Ltd recently subscribed to an easy listening music service at its factory, hoping that this would relax the workers and lead to greater productivity Divya is skeptical about this hypothesis and fears the music will be distracting, leading to lower productivity She sampled weekly production for the same six workers before the music was installed and after it was installed Her data are given below At  = 0.02, has the average production changed at all? Employee Week without music 219 205 226 198 209 216 Week with music 235 186 240 203 221 205 [Ans.: t= 0.478 ( x = 2.83), tCRIT  3.365( xCRIT  19.95) so not reject H o ] Proportion Question 47: On Friday, 11 stocks in a random sample of 40 of the roughly 2500 stocks traded on the New York Stock Exchange advanced; that is, their price of their shares increased In a sample of 60 NYSE stocks taken on Thursday, 24 advanced At  = 0.10, can you conclude that a smaller proportion of NYSE stocks advanced on Friday than did on Thursday? [Ans.: z = -1.283 ( p1  p  0.125), zL  1.28(( p1  p  0.1247) , so reject H o , a smaller proportion advanced on Friday] Question 48: A coal-fired power plant is considering two different systems for pollution abatement The first system has reduced the emission of pollutants to acceptable levels 68 percent of the time, as determined Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Operations Research - 379 - from 200 samples The second, more expensive system has reduced the emission of pollutants to acceptable levels 76 percent of the time, as determined 250 air samples If the expensive system is significantly more effective than the inexpensive system in reducing pollutants to acceptable levels, then the management of power plant will install the expensive system, Which system will be installed if management uses a significance level of 0.02 in making its decision? [Ans.: z = -1.89 ( p1  p  0.08), zL  2.05(( p1  p )L  0.0869) , so don’t reject H o , install the less expensive system.] Question 49: Two different areas of a large eastern city are being considered as sites for day-care centers Of 200 households surveyed in one section, the proportion in which the mother worked full-time was 0.52 In the other section, 40 percent of the 150 households surveyed had mothers working at full-time jobs At the 0.04 level of significance, is there a significant difference in the proportions of working mothers in the two areas of the city? [Ans.: z = 2.23 ( p1  p  0.12), zCRIT  2.05(( p1  p )CRIT  0.1105) , so reject H o , proportions are significantly different] Chi-square and analysis of variance Chi-square distribution is use to examine the difference among more than two sample proportions, ANOVA enables us to test for the significance of the differences among more than two sample means Chi-square,    (Oi  Ei )2 Ei where, Ei =Expected frequency & Oi is Observed frequency Number of degrees of freedom = (no of rows-1)×(no of columns-1) Question 50: Given the following dimensions for contingency tables, how many degrees of freedom will the chi-square statistic for each have? (a) rows, columns (b) rows, columns (c) rows, columns (d) rows, columns [Ans.: (a) 12 (b) (c) 12 (d) 9] Question 51: A brand manager is concerned that her brand’s share may be unevenly distributed throughout the country In a survey in which the country was divided into four geographic regions, a random sampling of 100 consumers in each region was surveyed, with the following results: Region NE NW SE SW TOTAL Purchase the brand 40 55 45 50 190 Do not purchase 60 45 55 50 210 Total 100 100 100 100 400 Develop a table of observed and expected frequencies for this problem (a) Calculate the sample  value (b) State the null and alternative hypothesis (c) If the level of significance is 0.05, should the null hypothesis be rejected? [Ans.: (a)  = 5.012 (b) H : region and purchasing are independent H : region and purchasing are dependent (c) U2 =7.815] Question 52: To see if silicon chip sales are independent of where the U.S economy is in the business cycle, data have been collected on the weekly sales of Zippy Chippy, a Silicon Valley firm, and on whether the U.S Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Sampling & Test of Hypothesis - 380 - economy was rising to a cycle peak, at a cycle peak, falling to a cycle trough, or at cycle trough The results are: Economy At peak At trough Rising Falling TOTAL High 20 30 20 30 100 WEEKLY CHIP SALES Medium 40 60 Low 30 40 TOTAL 30 100 30 40 200 Calculate a table of observed and expected frequencies for this problem (a) State the null and alternative hypothesis (b) Calculate the sample  value (c) At the 0.10 significance level, what is your conclusion? [Ans.: (a) H : sales and economy are independent H : sales and economy are dependent (b)  = 34.597 (c) U2 =10.645, so we reject H ] Question 53: A newspaper publisher, trying to pinpoint his market’s characteristics, wondered whether newspaper readership in the community is related to reader’s educational achievement A survey questioned adults in the area on their level of education and their frequency of readership The results are shown in the following table FREQUENCY OF READERSHIP Never Sometimes Morning or evening Both editions TOTAL LEVEL OF EDUCATION ACHIEVEMENT Professional College High school Did not or graduate grad complete high postgraduate school 10 17 11 21 12 23 35 38 16 28 85 19 97 41 13 46 TOTAL 59 48 96 66 269 At the 0.10 significance level, does the frequency of newspaper readership in the community differ according to the reader’s level of education? [Ans.:  = 32.855, U2 =14.684, so we reject H Different levels of education correspond to different frequencies of readership.] Question 54: The contingency table below summarize the results obtained in a study conducted by a research organization with respect to the performance of four competing brands of tooth paste among the users Brand A Brand B Brand C Brand D Total No of Cavities 13 17 11 50 One of five 63 70 85 82 300 More than five 28 37 48 37 150 Total 100 120 150 130 500 Test the hypothesis that incidence of cavities is independent of the brand of the tooth paste used Use level of significance 1% and 5% [Ans.:  = 1.911, U2 =12.59, so we accept H Hence, incidence of cavities is independent of the brand of the tooth paste used.] Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Operations Research - 381 - Question 55: Given below in the contingency table for production is three shifts and the number of defective good turn out- Find the value of  Is it possible that the number defective goods depends on the shifts run by them, No of Shifts: Shift I Week II Week III Week Total I 15 20 40 II 20 10 20 50 III 25 15 20 60 60 30 60 150 [Ans.:  = 3.647, U2 =9.488, so we accept H Hence, the number of defective does not depends on the shift run by the factory] (RTP-June/09) Analysis of Variance (ANOVA) One Way Classification: Sum of Squares for Columns, SSC =  n( x  x ) Mean Sum of Squares for Columns, MSC  Sum of Squares due to error, SSE = SSC c 1  ( x i ij  x j )2 j Mean Sum of Squares due to error, MSE  SSE t c MSC MSE Degree of Freedom between Columns = c-1 Degree of Freedom between Rows = t-c Variance Ratio, F  where, x = grand mean i.e mean of means, c = total no of columns r = total no of rows i = no of row j = no of column Question 56: The three samples below have been obtained from national populations with equal variances 12 10 10 13 14 12 11 14 Test the hypothesis at 5% level that the population means are equal (The table value of F at 5% level of significance for v =2 and v =12 is 3.88) [Ans.: F = 4, The table values of F at 5% level of significance for (2, 12) degrees of freedom is 3.88 The calculated value of F is more than the table value of F Hence, The null hypotheses is rejected We, therefore conclude that the population means are not equal.] Question 57: Below are given the yield (in kg.) per acre for trial plots an analysis of variance and state conclusion Treatment Plot no 42 48 50 66 62 68 Ph.: +91 11 47665555 of varieties of treatment Carry out 68 52 76 80 94 78 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Sampling & Test of Hypothesis - 382 - 34 52 78 70 64 70 82 66 [Ans.: F = 8.3, The table values of F at 5% level of significance for (3, 16) degrees of freedom is 3.24 The calculated value of F is more than the table value of F Hence, The null hypotheses is rejected Hence, The (RTP-Nov/08) treatment does not have same effect.] [Note: ICAI has assumed that one way classification should be used in above question instead of manifold classification] Question 58: The manager of an assembly line in a clock manufacturing plant decided to study how different speeds of the conveyor belt affect the rate of defective units produced in an 8-hour shift To examine this, he ran the belt at four different speeds for five 8-hour shifts each and measured the number of defective units found at the end of each shift The results of the study follow: Defective Units per Shift Speed Speed 27 32 32 36 32 33 34 34 30 40 Speed 37 35 38 36 34 Speed 35 27 33 31 29 (a) Calculate the mean number of defective units, x , for each speed; then determine the grand mean, x (b) Estimate the population variance (the between column variance) (i.e MSC) (c) Calculate the variances within the samples and estimate the population variance based upon these variances (the within column variance) (i.e MSE) (d) Calculate the F ratio At the 0.05 level of significance, the four conveyor-belt speeds produce the same mean rate of defective clocks per shift? [Ans.: (a) x j =36.31, 31,35,31; x = 33.25 (b) 34.5833 (c) 7.375 (d) F= 4.69, F U = 3.24, so we reject H o ] Manifold Classification: T2 Correction Factor, C  r c Sum of Squares between columns, SSC   Sum of Squares between rows, SSR   r (  x j )2 nj (  xi )2 ni C C c Total Sum of Squares, SST   xij2  C i 1 j 1 Sum of Squares due to Error, SSE = SST-{SSC+SSR} Degree of Freedom between Columns = c-1 Degree of Freedom between Rows = r-1 Degree of Freedom for total = rc-1 Degree of Freedom between errors = [rc-1]-[(c-1)+(r-1)] where, T = grand total c = total no of columns r = total no of rows i = no of row j = no of column Question 59: A farmer applies three types of fertilizers on separate plots The figures on yield per acre are tabulated below: Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Operations Research - 383 - Yield Fertilizers/Plots A B C D Total Nitrogen 24 Potash 6 28 Phosphates 10 32 Total 21 15 24 24 84 Find out if the plots are materially different in fertility as also if the three fertilizers make any material difference in yields ANOVA TABLE [Ans.: Sources of variation d.f S.S MSS Variance Ratio (F) Rows (Fertilizers) MSR=4 2.4 Columns (Plots) 18 MSC=6 3.6 Errors 10 MSE=1.667 Total 11 36 F (0.05, 3, 6) is 4.76 & F (0.05, 2, 6) is 5.14 The calculated value of F is less than the table value of F Hence, The null hypotheses is accepted.] Question 60: For the following data representing the number of units of production per day turned out by five workers using from machines, set-up the ANOVA table (Assumed Origin at 20) Workers Machine Type A B C D -2 -4 12 3 -6 -4 -8 -2 -7 -2 -1 (RTP-June/09) ANOVA TABLE [Ans.: Sources of variation d.f S.S MSS Variance Ratio (F) Rows (Workmen) 161.5 40.38 6.576 Columns (Machine) 33.8 112.93 18.39 Errors 12 73.7 6.14 Total 19 574 F (0.05, 4, 12) is 3.259 & F (0.05, 3, 12) is 3.49 The calculated value of F is more than the table value of F Hence, The null hypotheses is rejected.] Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -a- Table for Areas Under the Standard Normal Curve from to Z (Type II) [P (0 ≤ X ≤ x) = n (0 ≤ Z ≤ z)] z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3304 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 3.6 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 3.7 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -b- Student’s t Distribution The following table provides the values of t  that correspond to a given upper-tail area  and a specified number of degree of freedom (i.e n-1) Degree of Freedom( ) 0.25 0.2 0.15 0.1 0.05 Upper-tail area  0.025 0.01 0.005 0.0025 0.001 0.0005 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 80 100 120 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.679 0.678 0.677 0.677 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.849 0.848 0.846 0.845 0.845 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.047 1.045 1.043 1.042 1.041 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.299 1.296 1.292 1.290 1.289 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.676 1.671 1.664 1.660 1.658 12.710 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.009 2.000 1.990 1.984 1.980 31.820 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.403 2.390 2.374 2.364 2.358 63.660 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.678 2.660 2.639 2.626 2.617 127.300 14.090 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 2.971 2.937 2.915 2.887 2.871 2.860 318.300 22.330 10.210 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.261 3.232 3.195 3.174 3.160 636.600 31.600 12.920 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.767 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.496 3.460 3.416 3.390 3.373 ∞ 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291 Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -c- df 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0.995 0.000 0.010 0.072 0.207 0.412 0.676 0.989 1.344 1.735 2.156 2.603 3.074 3.565 4.075 4.601 5.142 5.697 6.265 6.844 7.434 8.034 8.643 9.260 9.886 10.520 11.160 11.808 12.461 13.121 13.787 0.99 0.000 0.020 0.115 0.297 0.554 0.872 1.239 1.647 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 6.408 7.015 7.633 8.260 8.897 9.542 10.196 10.856 11.524 12.198 12.879 13.565 14.256 14.953 0.975 0.001 0.051 0.216 0.484 0.831 1.237 1.690 2.180 2.700 3.247 3.816 4.404 5.009 5.629 6.262 6.908 7.564 8.231 8.907 9.591 10.283 10.982 11.689 12.401 13.120 13.844 14.573 15.308 16.047 16.791 0.95 0.004 0.103 0.352 0.711 1.145 1.635 2.167 2.733 3.325 3.940 4.575 5.226 5.892 6.571 7.261 7.962 8.672 9.390 10.117 10.851 11.591 12.338 13.091 13.848 14.611 15.379 16.151 16.928 17.708 18.493 0.9 0.016 0.211 0.584 1.064 1.610 2.204 2.833 3.490 4.168 4.865 5.578 6.304 7.042 7.790 8.547 9.312 10.085 10.865 11.651 12.443 13.240 14.041 14.848 15.659 16.473 17.292 18.114 18.939 19.768 20.599 0.75 0.102 0.575 1.213 1.923 2.675 3.455 4.255 5.071 5.899 6.737 7.584 8.438 9.299 10.165 11.037 11.912 12.792 13.675 14.562 15.452 16.344 17.240 18.137 19.037 19.939 20.843 21.749 22.657 23.567 24.478 Ph.: +91 9891 432 632 Upper-tail area  0.5 0.25 0.1 0.455 1.323 2.706 1.386 2.773 4.605 2.366 4.108 6.251 3.357 5.385 7.779 4.351 6.626 9.236 5.348 7.841 10.645 6.346 9.037 12.017 7.344 10.219 13.362 8.343 11.389 14.684 9.342 12.549 15.987 10.341 13.701 17.275 11.340 14.845 18.549 12.340 15.984 19.812 13.339 17.117 21.064 14.339 18.245 22.307 15.339 19.369 23.542 16.338 20.489 24.769 17.338 21.605 25.989 18.338 22.718 27.204 19.337 23.828 28.412 20.337 24.935 29.615 21.337 26.039 30.813 22.337 27.141 32.007 23.337 28.241 33.196 24.337 29.339 34.382 25.336 30.435 35.563 26.336 31.528 36.741 27.336 32.620 37.916 28.336 33.711 39.087 29.336 34.800 40.256 0.05 3.841 5.991 7.815 9.488 11.071 12.592 14.067 15.507 16.919 18.307 19.675 21.026 22.362 23.685 24.996 26.296 27.587 28.869 30.144 31.410 32.671 33.924 35.172 36.415 37.652 38.885 40.113 41.337 42.557 43.773 0.025 5.024 7.378 9.348 11.143 12.833 14.449 16.013 17.535 19.023 20.483 21.920 23.337 24.736 26.119 27.488 28.845 30.191 31.526 32.852 34.170 35.479 36.781 38.076 39.364 40.646 41.923 43.195 44.461 45.722 46.979 0.02 5.412 7.824 9.837 11.668 13.388 15.033 16.622 18.168 19.679 21.161 22.618 24.054 25.472 26.873 28.259 29.633 30.995 32.346 33.687 35.020 36.343 37.659 38.968 40.270 41.566 42.856 44.140 45.419 46.693 47.962 0.01 6.635 9.210 11.345 13.277 15.086 16.812 18.475 20.090 21.666 23.209 24.725 26.217 27.688 29.141 30.578 32.000 33.409 34.805 36.191 37.566 38.932 40.289 41.638 42.980 44.314 45.642 46.963 48.278 49.588 50.892 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta 0.005 7.879 10.597 12.838 14.860 16.750 18.548 20.278 21.955 23.589 25.188 26.757 28.300 29.819 31.319 32.801 34.267 35.718 37.156 38.582 39.997 41.401 42.796 44.181 45.559 46.928 48.290 49.645 50.993 52.336 53.672 -d- F Table for alpha=.10 df for numerator(v ) df for denominator(v ) 10 12 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 39.863 8.526 5.538 4.545 4.060 3.776 3.589 3.458 3.360 3.285 3.225 3.177 3.136 3.102 3.073 3.048 3.026 3.007 2.990 2.975 2.961 2.949 2.937 2.927 2.918 2.909 2.901 2.894 2.887 2.881 2.835 2.791 2.748 49.500 9.000 5.462 4.325 3.780 3.463 3.257 3.113 3.006 2.924 2.860 2.807 2.763 2.726 2.695 2.668 2.645 2.624 2.606 2.589 2.575 2.561 2.549 2.538 2.528 2.519 2.511 2.503 2.495 2.489 2.440 2.393 2.347 53.593 9.162 5.391 4.191 3.619 3.289 3.074 2.924 2.813 2.728 2.660 2.606 2.560 2.522 2.490 2.462 2.437 2.416 2.397 2.380 2.365 2.351 2.339 2.327 2.317 2.307 2.299 2.291 2.283 2.276 2.226 2.177 2.130 55.833 9.243 5.343 4.107 3.520 3.181 2.961 2.806 2.693 2.605 2.536 2.480 2.434 2.395 2.361 2.333 2.308 2.286 2.266 2.249 2.233 2.219 2.207 2.195 2.184 2.174 2.165 2.157 2.149 2.142 2.091 2.041 1.992 57.240 9.293 5.309 4.051 3.453 3.108 2.883 2.726 2.611 2.522 2.451 2.394 2.347 2.307 2.273 2.244 2.218 2.196 2.176 2.158 2.142 2.128 2.115 2.103 2.092 2.082 2.073 2.064 2.057 2.049 1.997 1.946 1.896 58.204 9.326 5.285 4.010 3.405 3.055 2.827 2.668 2.551 2.461 2.389 2.331 2.283 2.243 2.208 2.178 2.152 2.130 2.109 2.091 2.075 2.061 2.047 2.035 2.024 2.014 2.005 1.996 1.988 1.980 1.927 1.875 1.824 58.906 9.349 5.266 3.979 3.368 3.014 2.785 2.624 2.505 2.414 2.342 2.283 2.234 2.193 2.158 2.128 2.102 2.079 2.058 2.040 2.023 2.008 1.995 1.983 1.971 1.961 1.952 1.943 1.935 1.927 1.873 1.819 1.767 59.439 9.367 5.252 3.955 3.339 2.983 2.752 2.589 2.469 2.377 2.304 2.245 2.195 2.154 2.119 2.088 2.061 2.038 2.017 1.999 1.982 1.967 1.953 1.941 1.929 1.919 1.909 1.900 1.892 1.884 1.829 1.775 1.722 59.858 9.381 5.240 3.936 3.316 2.958 2.725 2.561 2.440 2.347 2.274 2.214 2.164 2.122 2.086 2.055 2.028 2.005 1.984 1.965 1.948 1.933 1.919 1.906 1.895 1.884 1.874 1.865 1.857 1.849 1.793 1.738 1.684 60.195 9.392 5.230 3.920 3.297 2.937 2.703 2.538 2.416 2.323 2.248 2.188 2.138 2.095 2.059 2.028 2.001 1.977 1.956 1.937 1.920 1.904 1.890 1.877 1.866 1.855 1.845 1.836 1.827 1.819 1.763 1.707 1.652 60.705 9.408 5.216 3.896 3.268 2.905 2.668 2.502 2.379 2.284 2.209 2.147 2.097 2.054 2.017 1.985 1.958 1.933 1.912 1.892 1.875 1.859 1.845 1.832 1.820 1.809 1.799 1.790 1.781 1.773 1.715 1.657 1.601 Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -e- F Table for alpha=.05 df for numerator(v ) df for denominator(v ) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 10 12 161.448 199.500 215.707 224.583 230.162 233.986 236.768 238.883 240.543 241.882 243.906 18.513 19.000 19.164 19.247 19.296 19.330 19.353 19.371 19.385 19.396 19.413 10.128 9.552 9.277 9.117 9.014 8.941 8.887 8.845 8.812 8.786 8.745 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5.912 6.608 5.786 5.410 5.192 5.050 4.950 4.876 4.818 4.773 4.735 4.678 5.987 5.143 4.757 4.534 4.387 4.284 4.207 4.147 4.099 4.060 4.000 5.591 4.737 4.347 4.120 3.972 3.866 3.787 3.726 3.677 3.637 3.575 5.318 4.459 4.066 3.838 3.688 3.581 3.501 3.438 3.388 3.347 3.284 5.117 4.257 3.863 3.633 3.482 3.374 3.293 3.230 3.179 3.137 3.073 4.965 4.103 3.708 3.478 3.326 3.217 3.136 3.072 3.020 2.978 2.913 4.844 3.982 3.587 3.357 3.204 3.095 3.012 2.948 2.896 2.854 2.788 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 2.687 4.667 3.806 3.411 3.179 3.025 2.915 2.832 2.767 2.714 2.671 2.604 4.600 3.739 3.344 3.112 2.958 2.848 2.764 2.699 2.646 2.602 2.534 4.543 3.682 3.287 3.056 2.901 2.791 2.707 2.641 2.588 2.544 2.475 4.494 3.634 3.239 3.007 2.852 2.741 2.657 2.591 2.538 2.494 2.425 4.451 3.592 3.197 2.965 2.810 2.699 2.614 2.548 2.494 2.450 2.381 4.414 3.555 3.160 2.928 2.773 2.661 2.577 2.510 2.456 2.412 2.342 4.381 3.522 3.127 2.895 2.740 2.628 2.544 2.477 2.423 2.378 2.308 4.351 3.493 3.098 2.866 2.711 2.599 2.514 2.447 2.393 2.348 2.278 4.325 3.467 3.073 2.840 2.685 2.573 2.488 2.421 2.366 2.321 2.250 4.301 3.443 3.049 2.817 2.661 2.549 2.464 2.397 2.342 2.297 2.226 4.279 3.422 3.028 2.796 2.640 2.528 2.442 2.375 2.320 2.275 2.204 4.260 3.403 3.009 2.776 2.621 2.508 2.423 2.355 2.300 2.255 2.183 4.242 3.385 2.991 2.759 2.603 2.490 2.405 2.337 2.282 2.237 2.165 4.225 3.369 2.975 2.743 2.587 2.474 2.388 2.321 2.266 2.220 2.148 4.210 3.354 2.960 2.728 2.572 2.459 2.373 2.305 2.250 2.204 2.132 4.196 3.340 2.947 2.714 2.558 2.445 2.359 2.291 2.236 2.190 2.118 4.183 3.328 2.934 2.701 2.545 2.432 2.346 2.278 2.223 2.177 2.105 4.171 3.316 2.922 2.690 2.534 2.421 2.334 2.266 2.211 2.165 2.092 4.085 3.232 2.839 2.606 2.450 2.336 2.249 2.180 2.124 2.077 2.004 4.001 3.150 2.758 2.525 2.368 2.254 2.167 2.097 2.040 1.993 1.917 3.920 3.072 2.680 2.447 2.290 2.175 2.087 2.016 1.959 1.911 1.834 Ph.: +91 9891 432 632 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -f- LOGARITHMS 10 0000 0043 0086 0128 0170 0212 0253 0294 0334 11 12 13 14 15 0414 0792 1139 1461 1761 0453 0828 1173 1492 1790 0492 0864 1206 1523 1818 0531 0899 1239 1553 1847 0569 0934 1271 1584 1875 0607 0969 1303 1614 1903 0645 1004 1335 1644 1931 0682 1038 1367 1673 1959 16 17 18 19 20 2041 2304 2553 2788 3010 2068 2330 2577 2810 3032 2095 2355 2601 2833 3054 2122 2380 2625 2856 3075 2148 2405 2648 2878 3096 2175 2430 2672 2900 3118 2201 2455 2695 2923 3139 21 22 23 24 25 3222 3424 3617 3802 3979 3243 3444 3636 3820 3997 3263 3464 3655 3838 4014 3284 3483 3674 3856 4031 3304 3502 3692 3874 4048 3324 3522 3711 3892 4065 26 27 28 29 30 4150 4314 4472 4624 4771 4166 4330 4487 4639 4786 4183 4346 4502 4654 4800 4200 4362 4518 4669 4814 4216 4378 4533 4683 4829 31 32 33 34 35 4914 5051 5185 5315 5441 4928 5065 5198 5328 5453 4942 5079 5211 5340 5465 4955 5092 5224 5353 5478 36 37 38 39 40 5563 5682 5798 5911 6021 5575 5694 5808 5922 6031 5587 5705 5821 5933 6042 41 42 43 44 45 6128 6232 6335 6435 6532 6138 6243 6345 6444 6542 46 47 48 49 50 6628 6721 6812 6902 6990 51 52 53 54 55 Mean Differences 17 21 25 29 0374 12 0719 1072 1399 1703 1987 0755 1106 1430 1732 2014 3 3 6 11 10 10 15 14 13 12 11 19 17 16 15 14 23 21 19 18 17 2227 2480 2718 2945 3160 2253 2504 2742 2967 3181 2279 2529 2765 2989 3201 2 2 5 4 7 11 10 9 13 12 12 11 11 3345 3541 3729 3909 4082 3365 3560 3747 3927 4099 3385 3579 3766 3945 4116 3404 3598 3784 3962 4133 2 2 4 4 6 5 8 7 4232 4393 4548 4698 4843 4249 4409 4564 4713 4857 4265 4425 4579 4728 4871 4281 4440 4594 4742 4886 4298 4456 4609 4757 4900 2 1 3 3 5 4 4969 5105 5237 5366 5490 4983 5119 5250 5378 5502 4997 5132 5263 5391 5514 5011 5145 5276 5403 5527 5024 5159 5289 5416 5539 5038 5172 5302 5428 5551 1 1 3 3 5599 5717 5832 5944 6053 5611 5729 5843 5955 6064 5623 5740 5855 5966 6075 5635 5752 5866 5977 6085 5647 5763 5877 5988 6096 5658 5775 5888 5999 6107 5670 5786 5899 6010 6117 1 1 6149 6253 6355 6454 6551 6160 6263 6365 6464 6561 6170 6274 6375 6474 6571 6180 6284 6385 6484 6580 6191 6294 6395 6493 6590 6201 6304 6405 6503 6599 6212 6314 6415 6514 6609 6222 6325 6425 6522 6618 6637 6730 6821 6911 6998 6646 6739 6830 6920 7007 6656 6749 6839 6928 7016 6665 6758 6848 6937 7024 6675 6767 6857 6946 7033 6684 6776 6866 6955 7042 6693 6785 6875 6964 7050 6702 6794 6884 6972 7059 7076 7160 7243 7324 7404 7083 7168 7251 7332 7412 7093 7177 7259 7340 7419 7101 7185 7267 7348 7427 7110 7193 7275 7356 7435 7118 7202 7284 7364 7443 7126 7210 7292 7372 7451 7135 7318 7300 7350 7459 56 57 58 59 60 7482 7559 7634 7709 7782 7490 7566 7642 7716 7789 7497 7574 7619 7723 7796 7505 7582 7657 7731 7803 7513 7589 7664 7738 7810 7520 7597 7672 7745 7818 7528 7604 7679 7752 7825 61 7853 7860 7868 7875 7882 7889 7896 Ph.: +91 9891 432 632 33 37 26 24 23 21 20 30 28 26 24 22 34 31 29 27 25 16 15 14 13 13 18 17 16 16 15 21 20 19 18 17 24 22 21 20 19 10 10 9 12 12 11 11 10 14 14 13 12 12 16 15 15 14 14 18 17 17 16 15 6 6 8 7 10 9 9 11 11 11 10 10 13 13 12 12 11 15 14 14 13 13 4 4 5 5 7 6 8 8 10 9 9 11 11 10 10 10 12 12 12 11 11 2 2 3 3 5 4 6 5 7 7 8 8 10 9 9 11 10 10 10 10 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 6712 6803 6893 6981 7067 1 1 2 2 3 3 4 5 4 5 5 6 6 7 7 8 8 7143 7226 7308 7355 7466 7152 7235 7316 73 7474 1 1 2 2 3 2 3 3 4 4 5 5 6 6 7 6 7 7 7536 7612 7686 7760 7832 7543 7619 7694 7767 7839 7551 7627 7701 7774 7846 1 1 2 1 2 2 3 3 4 4 5 4 5 5 6 6 7 7 7903 7910 7917 1 4 6 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -g- 62 63 64 65 7924 7993 8062 8129 7931 8000 8069 8136 7938 8007 8075 8142 7945 8014 8082 8149 7952 8021 8089 8156 7959 8028 8096 8162 7966 8035 8102 8169 7973 8041 8109 8176 7980 8048 8116 8182 66 67 68 69 70 8195 8261 8325 8388 8451 8202 8267 8331 8395 8457 8209 8274 8338 8401 8463 8215 8280 8344 8407 8470 8222 8287 8351 8414 8476 8228 8293 8357 8420 8482 8235 8299 8363 8426 8488 8241 8306 8370 8432 8494 71 72 73 74 75 8513 8573 8633 8692 8751 8519 8579 8639 8698 8756 8525 8585 8645 8704 8762 8531 8591 8651 8710 8768 8537 8597 8657 8716 8774 8543 8603 8663 8722 8779 8549 8609 8669 8727 8785 76 77 78 79 80 8808 8865 8921 8976 9031 8814 8871 8927 8982 9036 8820 8876 8932 8987 9042 8825 8882 8938 8993 9047 8831 8887 8943 8998 9053 8837 8893 8949 9004 9058 81 82 83 84 85 9085 9138 9191 9243 9294 9090 9143 9196 9248 9299 9096 9149 9201 9253 9304 9101 9154 9206 9258 9309 9106 9159 9212 9263 9315 86 87 88 89 90 9345 9395 9445 9494 9542 9350 9400 9450 9499 9547 9355 9405 9455 9504 9552 9360 9410 9460 9509 9557 91 92 93 94 95 9590 9638 9685 9731 9777 9595 9643 9689 9736 9782 9600 9647 9694 9741 9786 96 97 98 99 9823 9868 9982 9956 9827 9872 9917 9961 9832 9877 9921 9965 Mean Differences 3 1 3 3 7987 8055 8122 8189 1 1 1 1 2 2 8248 8312 8376 8439 8500 8254 8319 8382 8445 8506 1 1 1 1 1 2 2 3 2 3 3 8555 8615 8675 8733 8791 8561 8621 8681 8739 8797 8567 8627 8686 8745 8802 1 1 1 1 1 2 2 2 2 2 8842 8899 8954 9009 9063 8848 8904 8960 9015 9069 8854 8910 8965 9020 9074 8859 8915 8971 9025 9079 1 1 1 1 1 2 2 9112 9165 9217 9269 9320 9117 9170 9222 9274 9325 9122 9175 9227 9279 9330 9128 9180 9232 9284 9335 9133 9186 9238 9289 9340 1 1 1 1 1 9365 9415 9465 9513 9562 9370 9420 9469 9518 9566 9375 9425 9474 9523 9571 9380 9430 9479 9528 9576 9385 9435 9484 9533 9581 9390 9440 9489 9538 9586 0 0 9605 9652 9699 9745 9791 9609 9657 9703 9750 9795 9614 9661 9708 9754 9800 9619 9666 9713 9759 9805 9634 9671 9717 9763 9809 9628 9675 9722 9768 9814 9633 9680 9727 9773 9818 9836 9881 9928 9969 9841 9886 9930 9974 9845 9890 9934 9978 9850 9894 9939 9983 9854 9899 9943 9987 9859 9903 9948 9991 9863 9908 9952 9996 Ph.: +91 9891 432 632 5 5 5 6 6 4 4 5 4 5 5 6 6 3 3 4 4 4 4 5 5 5 5 5 2 2 3 3 3 3 3 4 4 4 4 5 5 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -h- ANTILOGARITHMS 00 01 02 03 04 05 1000 1023 1047 1072 1096 1122 1002 1026 1050 1074 1099 1125 1005 1018 1052 1076 1102 1127 1007 1030 1054 1079 1104 1130 1009 1033 1057 1081 1107 1132 1012 1035 1059 1084 1109 1135 1014 1038 1062 1086 1112 1138 1016 1040 1064 1089 1114 1140 1019 1042 1067 1091 1117 1143 06 07 08 09 10 1148 1175 1202 1230 1259 1151 1178 1205 1233 1262 1153 1180 1208 1236 1265 1156 1183 1211 1239 1268 1159 1186 1213 1242 1271 1161 1189 1216 1245 1274 1164 1191 1219 1247 1276 1167 1194 1222 1250 1279 11 12 13 14 15 1288 1318 1349 1380 1413 1291 1321 1352 1384 1416 1294 1324 1355 1387 1419 1297 1327 1358 1390 1422 1300 1330 1361 1393 1426 1303 1333 1364 1396 1429 1306 1337 1368 1400 1432 16 17 18 19 20 1445 1479 1514 1549 1585 1449 1483 1517 1552 1589 1452 1486 1521 1556 1592 1455 1489 1524 1560 1596 1459 1492 1528 1563 1600 1462 1493 1531 1567 1603 21 22 23 24 25 1622 1660 1698 1738 1778 1626 1663 1702 1742 1782 1629 1667 1706 1746 1786 1633 1671 1710 1750 1791 1637 1675 1714 1754 1795 26 27 28 29 30 1820 1862 1905 1950 1995 1824 1866 1910 1954 2000 1828 1871 1914 1959 2004 1832 1875 1919 1963 2009 31 32 33 34 35 2042 2089 2138 2188 2239 2046 2094 2143 2193 2245 2051 2099 2148 2198 2249 36 37 38 39 40 2291 2344 2399 2455 2512 2296 2350 2404 2460 2518 41 42 43 44 45 2570 2630 2692 2754 2818 46 47 48 49 50 51 52 Mean Differences 1 1 1 1 1 1 1 1 1021 1045 1069 1094 1119 1146 0 0 0 0 0 1 1 1 1 1169 1197 1225 1253 1282 1172 1199 1227 1256 1285 0 0 1 1 1 1 1 1 1 1 1 1 1309 1340 1371 1403 1435 1312 1343 1374 1406 1439 1315 1346 1377 1409 1442 0 0 1 1 1 1 1 1 1 1466 1496 1535 1570 1607 1469 1500 1538 1574 1611 1472 1503 1542 1578 1614 1476 1507 1545 1581 1618 0 0 1 1 1 1 1 1641 1679 1718 1758 1799 1644 1683 1722 1762 1803 1648 1687 1726 1766 1807 1652 1690 1730 1770 1811 1656 1694 1734 1774 1816 0 0 1 1 1837 1879 1923 1968 2014 1841 1884 1928 1972 2018 1845 1888 1932 1977 2023 1849 1892 1936 1982 2028 1854 1897 1941 1986 2032 1858 1901 1945 1991 2037 0 0 2056 2104 2153 2203 2254 2061 2109 2158 2208 2259 2065 2113 2163 2213 2265 2070 2118 2168 2218 2270 2075 2123 2173 2223 2275 2080 2128 2178 2228 2280 2084 2133 2183 2234 2286 2301 2355 2410 2465 2523 2307 2360 2415 2472 2529 2312 2366 2421 2477 2535 2317 2371 2427 2483 2541 2323 2376 2432 2489 2547 2328 2381 2438 2495 2553 2333 2386 2443 2500 2559 2576 2636 2698 2761 2825 2582 2642 2704 2767 2831 2588 2649 2710 2773 2838 2594 2655 2716 2780 2844 2600 2661 2723 2786 2851 2606 2667 2729 2793 2858 2612 2673 2735 2799 2864 2884 2951 3020 3090 3162 2891 2958 3027 3097 3170 2897 2965 3034 3105 3177 2904 2972 3041 3112 3184 2911 2979 3048 3119 3192 2917 2985 3055 3126 3199 2924 2992 3062 3133 3206 3236 3311 3243 3319 3251 3327 3258 3334 3266 3342 3273 3350 3281 3357 Ph.: +91 9891 432 632 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 3 3 1 1 2 2 2 2 2 2 2 3 3 3 3 3 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 4 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 2339 2393 2449 2506 2564 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 2618 2679 2742 2805 2871 2624 2685 2748 2812 2877 1 1 1 1 1 2 2 2 3 3 3 3 4 4 4 4 5 5 5 6 6 2931 2999 3069 3141 3214 2938 3006 3076 3148 3221 2944 3013 3083 3155 3228 1 1 1 1 1 2 2 3 3 3 4 4 4 4 5 5 5 6 6 6 3289 3365 3296 3373 3304 3381 1 2 2 3 4 5 5 6 8 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta -i- 53 54 55 3388 3467 3548 3396 3475 3556 3404 3483 3565 3412 3491 3573 3420 3499 3581 3428 3508 3589 3436 3516 3597 3443 3524 3606 3451 3532 3614 56 57 58 59 60 3631 3715 3802 3890 4074 3639 3724 3811 3899 4083 3648 3733 3819 3908 4093 3656 3741 3828 3917 4102 3664 3750 3837 3926 4111 3673 3758 3846 3936 4121 3681 3767 3855 3945 4130 3690 3776 3864 3954 4140 61 62 63 64 65 4074 4169 4266 4365 4467 4083 4178 4276 4375 4477 4093 4188 4285 4385 4487 4102 4198 4295 4395 4498 4111 4207 4305 4406 4508 4121 4217 4315 4416 4519 4130 4227 4325 4426 4529 66 67 68 69 70 4571 4677 4786 4898 5012 4581 4688 4797 4909 5023 4592 4699 4808 4920 5035 4603 4710 4819 4932 5047 4613 4721 4831 4943 5058 4624 4732 4842 4955 5070 71 72 73 74 75 5129 5248 5376 5495 5623 5140 5260 5383 5508 5636 5152 5272 5395 5521 5649 5164 5284 5408 5534 5662 5176 5297 5420 5546 5675 76 77 78 79 80 5754 5888 6026 6166 6310 5768 5902 6039 6180 6324 5781 5916 6053 6194 6339 5794 5929 6067 6209 6353 81 82 83 84 85 6457 6607 6761 6918 7079 6471 6622 6776 6934 7096 6486 6637 6792 6950 7112 86 87 88 89 90 7244 7413 7586 7762 7943 7261 7430 7603 7780 7962 91 92 93 94 95 8128 8318 8511 8710 8913 96 97 98 99 9120 9333 9550 9772 Mean Differences 5 3459 3540 3622 1 1 2 2 2 3698 3784 3873 3963 4150 3707 3793 3882 3972 4159 1 1 2 2 3 3 3 4 4 4 5 4140 4236 4335 4436 4539 4150 4256 4345 4446 4550 4159 4256 4355 4457 4560 1 1 2 2 3 3 4 4 4634 4742 4853 4966 5082 4645 4753 4864 4977 5093 4656 4764 4875 4989 5105 4667 4775 4887 5000 5117 1 1 2 2 3 3 5188 5309 5433 5559 5689 5200 5321 5445 5572 5702 5212 5333 5458 5585 5715 5224 5346 5470 5598 5728 5236 5358 5483 5610 5741 1 1 2 3 5808 5943 6081 6223 6368 5821 5957 6095 6237 6383 5834 5970 6109 6252 6397 5848 5984 6124 6266 6412 5861 5998 6138 6281 6427 5875 6012 6152 6295 6442 1 1 6501 6653 6808 6966 7129 6516 6668 6823 6982 7145 6531 6683 6839 6998 7161 6546 6699 6855 7015 7178 6561 6714 6871 7031 7194 6577 6730 6887 7047 7211 6592 6745 6902 7063 7228 7278 7447 7621 7798 7980 7295 7464 7638 7816 7998 7311 7482 7656 7834 8017 7328 7499 7674 7852 8035 7345 7516 7691 7870 8054 7362 7534 7709 7889 8072 7379 7551 7727 7907 8091 8147 8337 8531 8730 8933 8166 8356 8551 8750 8954 8185 8375 8570 8770 8974 8204 8395 8590 8790 8895 8222 8414 8610 8810 9016 8241 8433 8630 8831 9036 8260 8453 8650 8851 9057 9141 9354 9572 9795 9162 9376 9594 9817 9183 9397 9616 9840 9204 9419 9638 9863 9226 9441 9661 9886 9247 9462 9683 9908 9268 9484 9705 9931 Ph.: +91 9891 432 632 6 6 8 5 5 6 6 7 7 8 8 5 5 6 6 7 7 8 8 9 9 4 5 5 6 6 7 7 8 8 9 9 10 10 10 10 11 4 4 5 5 6 6 7 8 8 9 9 10 10 10 10 10 11 11 11 11 11 3 3 4 4 5 6 7 7 8 9 10 10 10 10 11 11 11 11 12 12 12 13 13 13 2 2 3 3 5 5 6 6 8 8 9 10 10 11 11 11 11 12 12 12 13 13 13 14 14 14 15 15 7396 7568 7745 7925 8110 2 2 3 4 5 5 7 7 9 9 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15 16 16 16 17 8279 8472 8670 8872 9078 8299 8492 8690 8892 9099 2 2 4 4 6 6 8 8 10 10 10 10 11 12 12 12 12 13 14 14 14 15 15 15 16 16 17 17 17 18 18 19 9290 9506 9727 9954 9311 9528 9750 9977 2 2 4 7 9 11 11 11 11 13 13 13 14 15 15 16 16 17 17 18 18 19 20 20 20 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta ... problem by applying Vogel's Approximation Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta... by management to spend in certain fixed cost Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta... can clean Ph.: +91 11 47665555 Paraggupta_ca@yahoo.co.in World’s largest CA Final student’s consultancy group: http://groups.yahoo.com/group/costingbyparaggupta Cost Accounting & Management -3-