Name of the Module PIE CHARTS & LINE GRAPHS - Sreenivasa ...

REASONING COURSEPie Charts & Line GraphsSREENIVASA INSTITUTE OF TECHNOLOGY ANDMANAGEMENT STUDIESMurukambattu Post, Chittoor – 517 127 (A.P)AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY –ANANTAPUR,Name of the ModulePIE CHARTS & LINE GRAPHSByA.SUSMITHA,EEE.SITAMS Page 1

REASONING COURSEPie Charts & Line GraphsMODULE OBJECTIVE:Pie charts:A pie chart (or a circle graph) is a circular chart divided into sectors, illustratingproportion. In a pie chart, the arc length of each sector (and consequently its centralangle and area), is proportional to the quantity it represents. When angles are measured with1 turn as unit then a number of percent is identified with the same number of centiturns.Together, the sectors create a full disk. It is named for its resemblance to a pie which hasbeen sliced. The earliest known pie chart is generally credited to William Playfair's StatisticalBreviary of 1801. Pie charts are common in business and journalism.Line graphs:A line graph is a way of visually representing related data where individual items of dataare plotted and joined by a line. They are useful for presenting data over time to comparechanges to a variable over set period. Joining up the points gives an instant picture of pasttrends (increases or decreases) and can be used to extrapolate those trends to makepredictions for future. The variable represented is continuous. A graph is set within 2 axes: x and y.The axes will not always start measuring from zero. If they don’t this is called thesuppression of zero. This will affect the appearance of the line(s) on the graph making themsteeper than they would be if the scale started at zero and occupied the same space as thescale would be smaller.PREREQUISITES (RELATED FORMULAS):In pie charts, from geometry, we know that the area the sector of a circle must beproportional to the corresponding value of the component.Since the sum of all the central angle is 360°, we haveCentral angle of the component = {(value of the component/Total value) x 360} °.SITAMS Page 2

REASONING COURSEPie Charts & Line GraphsSOLVED EXAMPLES:PIE CHARTS:Example 1-5:The following pie-charts show the distribution of students of graduate and post-graduatelevels in seven different institutes in a town. [Bank P.O. 2003]1. What is the total number of graduate and post-graduate level students is institute R?A. 8320 B. 7916C. 9116 D. 8099Answer: (D)Required number = (17% of 27300) + (14% of 24700)= 4641 + 3458= 8099.2. What is the ratio between the number of students studying at post-graduate and graduatelevels respectively from institute S?A. 14:19 B. 19:21C. 17:21 D. 19:14Answer: (D)Required ratio = (21% of 24700) = (21 x 24700) = 19(14% of 27300) 14 x 27300 143. How many students of institutes of M and S are studying at graduate level?A. 7516 B. 8463C. 9127 D. 9404Answer: (B)Students of institute M at graduate level= 17% of 27300 = 4641.Students of institute S at graduate level = 14% of 27300 = 3822.Total number of students at graduate in institutes M and S = (4641 + 3822)= 8463.SITAMS Page 3

REASONING COURSEPie Charts & Line Graphs4. What is the ratio between the number of students studying at post-graduate level frominstitutes S and the number of students studying at graduate level from institute Q?A. 13:19 B. 21:13C. 13:8 D. 19:13Answer: (D)Required ratio = (21% of 24700) = (21 x 24700) = 19 .(13% of 27300) 13 x 27300 135. Total number of students studying at post-graduate level from institutes N and P isA. 5601 B. 5944C. 6669 D. 8372Answer: (C)Required number = (15% of 24700) + (12% of 24700)= 3705 + 2964= 6669.Example 6-8:The following pie charts exhibit the distribution of the overseas tourist traffic from India. Thetwo charts show the tourist distribution by country and the age profiles of the touristsrespectively. [NABARD, 2001]Distribution of Overseas Tourist Traffic from India.6. What percentage of Indian tourist went to either USA or UK?A.40 % B.50 %C.60 % D.70 %Answer: (B)SITAMS Page 4

REASONING COURSEPie Charts & Line Graphs(40+10) = 50% (from first chart)7. The ratio of the number of Indian tourists that went to USA to the number of Indiantourists who were below 30 years of age is ?A.2:1B.8:3C.3:8D. cannot be determinedAnswer: (B)40:15 = 8:38. If amongst other countries, Switzerland accounted for 25% of the Indian tourist traffic, andit is known from official Swiss records that a total of 25 lakh Indian tourists had gone toSwitzerland during the year, then find the number of 30-39 year old Indian tourists who wentabroad in that year ?A. Rs.18.75 lakh B. Rs. 25 lakhC. Rs. 50 lakh D. Rs. 75 lakhAnswer: (D)Tourist traffic from other countries to Swiz is 20%.Amongst this 20%, 25% of traffic from India.So, 25% of 20% = 5% corresponds to the Indian traffic in Switzerland.5 % corresponds to Switzerland's 25 lakh. Hence 15% will be 75 lakh.LINE GRAPHS:Example 9-13Two different finance companies declare fixed annual rate of interest on the amounts investedwith them by investors. The rate of interest offered by these companies may differ from yearto year depending on the variation in the economy of the country and the banks rate ofinterest. The annual rate of interest offered by the two Companies P and Q over the years isshown by the line graph provided below. [Bank P.O. 2003]Annual Rate of Interest Offered by Two Finance Companies Over the Years.9. A sum of Rs. 4.75 lakhs was invested in Company Q in 1999 for one year. How muchmore interest would have been earned if the sum was invested in Company P?A.Rs 19,000 B.Rs.14, 250C.Rs.11, 750 D.Rs. 9,500Answer: (D)DIFFERENCE = Rs. [(10% of 4.75) - (8% of 4.75)]= Rs. (2% of 4.75) lakhs= Rs. 0.095 lakhs= Rs. 9500.10. If two different amounts in the ratio 8:9 are invested in Companies P and Q respectivelyin 2002, then the amounts received after one year as interests from Companies P and Q arerespectively in the ratio?SITAMS Page 5

REASONING COURSEPie Charts & Line GraphsA.2:3 B. 3:4C.6:7 D. 4:3Answer: (D)Let the amounts invested in 2002 in Companies P and Q be Rs. 8x and Rs. 9xrespectively.Then, interest received after one year= Rs. (6% of 8x)from Company P=Rs. 48 x.100and interest received after one year fromCompany Q= Rs. (4% of 9x)=Rs. 36 x.100Required ratio =48 x10036 x100= 4 .311. In 2000, a part of Rs. 30 lakhs was invested in Company P and the rest was invested inCompany Q for one year. The total interest received was Rs. 2.43 lakhs. What was theamount invested in Company P?A. Rs.9 lakh B. Rs.11 lakhC.Rs. 12 lakhD.Rs.18 lakhAnswer: (D)Let Rs. x lakhs be invested in Company P in 2000, the amount invested in Company Q in2000 = Rs. (30 - x) lakhs.Total interest received from the two Companies after 1 year= Rs. [(7.5% of x) + {9% of (30 - x)}] lakhs1.5x= Rs. 2.7 - lakhs.1001.5x2.7 - = 2.43 x = 18.10012. An investor invested a sum of Rs. 12 lakhs in Company P in 1998. The total amountreceived after one year was re-invested in the same Company for one more year. The totalappreciation received by the investor on his investment was?A. Rs. 2, 96,200 B. Rs. 2, 42,200C. Rs. 2, 25,600 D. Rs. 2, 16,000Answer: (C)Amount received from Company P after one year (i.e., in 199) on investing Rs. 12 lakhs in it= Rs. [12 + (8% of 12)] lakhs= Rs. 12.96 lakhs.Appreciation received on investment during the period of two years= Rs. (14.256 - 12) lakhs= Rs. 2.256 lakhs = Rs. 2, 25,600.SITAMS Page 6

REASONING COURSEPie Charts & Line Graphs13. An investor invested Rs. 5 lakhs in Company Q in 1996. After one year, the entireamount along with the interest was transferred as investment to Company P in 1997 for oneyear. What amount will be received from Company P, by the investor?A. Rs. 5, 94,550 B. Rs. 5, 80,425C. Rs. 5, 77,800 D. Rs. 5, 77,500Answer: (B)Amount received from Company Q after one year on investment of Rs. 5 lakhs in the year1996= Rs. [5 + (6.5% of 5)] lakhs= Rs. 5.325 lakhs.Amount received from Company P after one year on investment of Rs. 5.325 lakhs in theyear 1997= Rs. [5.325 + (9% of 5.325)] lakhs= Rs. 5.80425 lakhs= Rs. 5, 80, 425.Example: 14-19The following line graph gives the annual percent profit earned by a Company during theperiod 1995 - 2000. [R.B.I. 2003]Percent Profit Earned by a Company over the Years.%Profit = Income - Expenditure x 100Expenditure14. If the expenditures in 1996 and 1999 are equal, then the approximate ratio of the incomein 1996 and 1999 respectively is?A.1:1 B. 2:3C.13:14 D. 9:10Answer: (D)Let the expenditure in 1996 = x.Also, let the incomes in 1996 and 1999 be I1 and I2 respectively.Then, for the year 1996, we have:55 = I 1 - x x 10055 =I 1- 1 I1 = 155x ... (i)x 100 x 10070 = I 2 - x 70 I 2x 100 = - 1 I2 = 170x ... (ii)x 100 x 100From (i) and (ii), we get:155xI1 =I2100170x100= 155 0.91 9 : 10.170 1SITAMS Page 7

REASONING COURSEPie Charts & Line Graphs15. If the income in 1998 was Rs. 264 crores, what was the expenditure in 1998?A. Rs. 104 crores B. Rs. 145 croresC. Rs. 160 crores D. Rs. 185 croresAnswer: (C)Let the expenditure is 1998 be Rs. x crores.Then, 65 = 264 - x x 100x65 264 = - 1100 xx = 264 x 100 = 160.165Expenditure in 1998 = Rs. 160 crores.16. In which year is the expenditure minimum?A. 2000 B. 1997C. 1996 D. Cannot be determinedAnswer: (D)The line-graph gives the comparison of percent profit for different years.But the comparison of the expenditures is not possible without more data.Therefore, the year with minimum expenditure cannot be determined.17. If the profit in 1999 was Rs. 4 crores, what was the profit in 2000?A. Rs. 4.2 crores B. Rs. 6.2 croresC. Rs. 6.8 crores D. Cannot be determinedAnswer: (D)From the line-graph we obtain information about the percentage profit only. To find the profitin 2000 we must have the data for the income or expenditure in 2000.Therefore, the profit for 2000 cannot be determined.18. What is the average profit earned for the given years?A. 50 2/3 B. 55 5/6C. 60 1/6 D. 33 5/3Answer: (B)Average percent profit earned for the given years= 1 x [40 + 55 + 45 + 65 + 70 + 60] = 335 = 55 5 .6 6 6SITAMS Page 8

REASONING COURSEPie Charts & Line GraphsEXERCISE PROBLEMS:PIE CHARTS:Problem 1-3:The following pie chart gives the information about the distribution of weight in the humanbody according to different kinds of components. Study the pie charts and answer thequestion.Distribution of Weight in Human Body1. What percentage of proteins of the human body is equivalent to the weight of its skin?A. 41.66 % B. 43.33 %C. 44.44% D. Cannot be determined2. How much of the human body is neither made of bones or skin?A. 40 % B. 50 %C. 60 % D. 70 %3. What is the ratio of the distribution of proteins in the muscles to that of the distribution ofproteins in the bones?A. 2:1 B. 2:3C. 3:2 D. Cannot be determinedProblem 4-6:The pie chart shows the distribution of New York market share by value of differentcomputer companies in 2005.SITAMS Page 9

REASONING COURSEPie Charts & Line GraphsThe pie chart shows the distribution of New York market share by volume of differentcomputer companies in 2005.Number of units sold in 2005 in New York = 1,500Value of units sold in 2005 in New York = US $1,650,000.Distribution of New York market share by volume of different computer companies in 2005.4. For the year 2005, which company has realised the lowest average unit sales price for aPC?A. Commodore B. IBMC. Tandy D. Cannot be determined5. Over the period 2005-2006, if sales (value-wise) of IBM PC's increased by 50% and ofApple by 15% assuming that PC sales of all other computer companies remained the same,by what percentage (approximately) would the PC sales in New York (value -wise) increaseover the same period ?A. 16.1 % B. 18%C. 14 % D. None of these6. In 2005, the average unit sale price of an IBM PC was approximately (in US$)A. 3180 B. 2800C. 393 D. 3080Problem 7-11:The following pie-chart shows the sources of funds to be collected by the National HighwaysAuthority of India (NHAI) for its Phase II projects. Study the pie -chart and answers thequestion that follow.SITAMS Page 10

REASONING COURSEPie Charts & Line GraphsSources of funds to be arranged by NHAI for Phase II projects (in Rs.crores)7. Nearly about 20% of the funds are to be arranged through:A. SPVS B. External AssistanceC. Annuity D. Market Borrowing8. If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent(approximately) should it increase the Market Borrowing to arrange for the shortage offunds?A. 4.5 % B. 7.5 %C. 6 % D. 8 %9. If the toll is to be collected through an outsourced agency by allowing a maximum 10%commission, how much amount should be permitted to be collected by the outsourcedagency, so that the project is supported with Rs. 4910 crores?A. Rs. 6213 crores B. Rs. 5827 croresC. Rs. 5401 crores D. Rs. 5316 crores10. The central angle corresponding to Market Borrowing isA. 52° B. 137.8°C. 187.2° D. 192.4°11. The approximate ratio of the funds to be arranged through Toll and that through MarketBorrowing isA. 2:1 B. 1:6C. 3:11 D. 2:5Problem 12-15:The circle-graph given here shows the spending of a country on various sports during aparticular year. Study the graph carefully and answer the questions given below it.SITAMS Page 11

REASONING COURSEPie Charts & Line Graphs12. What percent of total spending is spent on Tennis?A.12 ½ % B.22 ½ %C.25%D.45%13. How much percent more is spent on Hockey than that on Golf?A.27 % B.37 %C.37.5 % D.75 %14. If the total amount spent on sports during the year be Rs. 1,80,00,000 , the amount spenton Basketball exceeds on Tennis by:A. Rs. 2, 50,000 B. Rs. 3, 60,000C.Rs.3, 75,000 D. Rs. 4, 10,00015. How much percent less is spent on Football than that on Cricket?A. 22 2/9 % B.27 %C.33 1/3 % D.37 1/7 %Problem 16-25:The following pie-chart shows the percentage distribution of the expenditure incurred inpublishing a book. Study the pie-chart and the answer the questions based on it.[Bank P.O. 2002]Various Expenditures (in percentage) Incurred in Publishing a Book16. If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, andthen what will be amount of royalty to be paid for these books?A. Rs. 19, 450 B. Rs. 21, 200C. Rs. 22, 950 D. Rs. 26, 15017. What is the central angle of the sector corresponding to the expenditure incurred onRoyalty ?A. 15° B. 24°C. 54° D. 48°18. The price of the book is marked 20% above the C.P. If the marked price of the book is RsA. Rs. 36 B. Rs. 37.5C. Rs. 42 D. Rs. 44.2519. If 5500 copies are published and the transportation cost on them amounts to Rs. 82500,then what should be the selling price of the book so that the publisher can earn a profit of25%?A. Rs. 187.50 B. Rs. 191.5C. Rs. 175 D. Rs. 18020. Royalty on the book is less than the printing cost by:A. 5% B. 33 1/5 %C.20 % D. 25 %SITAMS Page 12

REASONING COURSEPie Charts & Line Graphs21. If the difference between the two expenditures is represented by 18º in the pie-chart, thenthese expenditures possibly areA. Binding Cost and Promotion CostB. Paper Cost and RoyaltyC. Binding Cost and Printing CostD. Paper Cost and Printing Cost22. For an edition of 12,500 copies, the amount of Royalty paid by the publisher is Rs. 2,81,250. What should be the selling price of the book if the publisher desires a profit of 5%?A. Rs. 152.50 B. Rs. 157.50C. Rs. 162.50 D. Rs. 167.5023. If for an edition of the book, the cost of paper is Rs. 56250, then find the promotion costfor this edition.A. Rs. 20, 000 B. Rs. 22, 500C. Rs. 25, 500 D. Rs. 28, 12524. Which two expenditures together have central angle of 108º?A. Binding Cost and Transportation CostB. Printing cost and Paper CostC. Royalty and Promotion CostD. Binding Cost and Paper Cost25. What is the central angle of the sector corresponding to the expenditure incurred onprinting cost?A. 15° B. 24°C. 54° D.36°LINE GRAPHS:Problem 26-30: Study the following line graph and answer the questions. [S.B.I. P.O.2000]Exports from Three Companies over the Years (in Rs. crore)26. For which of the following pairs of years the total exports from the three Companiestogether are equal?A. 1995 and 1998 B. 1996 and 1998C. 1997 and 1998 D. 1995 and 199627. Average annual exports during the given period for Company Y is approximately whatpercent of the average annual exports for Company Z?A. 87.12 % B. 89.64 %C.91.21 % D. 93.33 %SITAMS Page 13

REASONING COURSEPie Charts & Line Graphs28. In which year was the difference between the exports from Companies X and Y theminimum?A. 1994 B. 1995C. 1996 D. 199729. What was the difference between the average exports of the three Companies in 1993 andthe average exports in 1998?A. Rs. 15.33 crores B. Rs. 18.67 croresC. Rs. 20 crores D. Rs. 22.17 crores30. In how many of the given years, were the exports from Company Z more than the averageannual exports over the given years?A. 2 B. 3C. 4 D. 5Problem 31-35:The following line graph gives the ratio of the amounts of imports by a company to theamount of exports from that company over the period from 1995 to 2001. [S.B.I. P.O. 2001]Ratio of Value of Imports to Exports by a Company over the Years.31. If the imports in 1998 were Rs. 250 crores and the total exports in the years 1998 and1999 together was Rs. 500 crores, then the imports in 1999 was?A. Rs. 250 crores B. Rs. 300 croresC. Rs. 357 crores D. Rs. 420 crores32. The imports were minimum proportionate to the exports of the company in the year ?A. 1995 B. 1996C. 1997 D. 200033. What was the percentage increase in imports from 1997 to 1998?A. 72 B. 56C. 28 D. Data inadequate34. If the imports of the company in 1996 was Rs. 272 crores, the exports from the companyin 1996 was?A. Rs. 370 crores B. Rs. 320 croresC. Rs. 280 crores D. Rs. 275 crores35. In how many of the given years were the exports more than the imports?A. 1 B. 2C. 3 D. 4SITAMS Page 14

REASONING COURSEPie Charts & Line GraphsProblem 36-40:Study the following line graph and answer the questions based on it. [R.B.I. 2003]Number of Vehicles Manufactured by Two companies over the Years(Number in Thousands)36. What is the difference between the number of vehicles manufactured by Company Y in2000 and 2001?A. 50, 000 B. 42, 000C. 33, 000 D. 21, 00037. What is the difference between the total productions of the two Companies in the givenyears ?A. 19, 000 B. 22, 000C. 26, 000 D. 28, 00038. What is the average numbers of vehicles manufactured by Company X over the givenperiod? (Rounded off to nearest integer)A. 1, 19, 333 B. 1, 13, 666C. 1, 12, 778 D. 1, 11, 22339. In which of the following years, the difference between the productions of Companies Xand Y was the maximum among the given years?A. 1997 B. 1998C. 1999 D. 200040. The production of Company Y in 2000 was approximately what percent of the productionof Company X in the same year?A. 173 B. 164C. 132 D. 97Problem 41-45The following line graph gives the percent profit earned by two Companies X and Y duringthe period 1996 - 2001. [NABARD, 2002]Percentage profit earned by Two Companies X and Y over the Given Years%Profit = Income - Expenditure x 100ExpenditureSITAMS Page 15

REASONING COURSEPie Charts & Line Graphs41. The incomes of two Companies X and Y in 2000 were in the ratio of 3:4 respectively.What was the respective ratio of their expenditures in 2000?A. 7:22 B. 14:19C. 15:22 D. 27:3542. If the expenditure of Company Y in 1997 was Rs. 220 crores, what was its income in1997?A. Rs. 312 crores B. Rs. 297 croresC. Rs. 283 crores D. Rs. 275 crores43. If the expenditures of Company X and Y in 1996 were equal and the total income of thetwo Companies in 1996 was Rs. 342 crores, what was the total profit of the two Companiestogether in 1996? (Profit = Income - Expenditure)A. Rs. 240 crores B. Rs. 171 croresC. Rs. 120 crores D. Rs. 102 crores44. The expenditure of Company X in the year 1998 was Rs. 200 crores and the income ofcompany X in 1998 was the same as its expenditure in 2001. The income of Company X in2001 was?A. Rs. 465 crores B. Rs. 385 croresC. Rs. 335 crores D. Rs. 295 crores45. If the incomes of two Companies were equal in 1999, then what was the ratio ofexpenditure of Company X to that of Company Y in 1999?A. 6:5 B. 5:6C. 11:6 D. 16:15Problem 46-50The following line graph gives the percentage of the number of candidates who qualified anexamination out of the total number of candidates who appeared for the examination over aperiod of seven years from 1994 to 2000.[Bank P.O. 2000]Percentage of Candidates Qualified to Appeared in an Examination overthe YearsSITAMS Page 16

REASONING COURSEPie Charts & Line Graphs46. The difference between the percentages of candidates qualified to appear was maximumin which of the following pairs of years?A. 1994 and 1995 B. 1997 and 1998C. 1998 and 1999 D. 1999 and 200047. In which pair of years was the number of candidates qualified the same?A. 1995 and 1997 B. 1995 and 2000C. 1998 and 1999 D. Data inadequate48. If the number of candidates qualified in 1998 was 21200, what was the number ofcandidates appeared in 1998?A. 32, 000 B. 28, 500C. 26, 500 D. 25, 00049. If the total number of candidates appeared in 1996 and 1997 together was 47400, then thetotal number of candidates qualified in these two years together was?A. 34, 700 B. 32, 100C. 31, 500 D. Data inadequate50. The total number of candidates qualified in 1999 and 2000 together was 33500 and thenumber of candidates appeared in 1999 was 26500. What was the number of candidates in2000?A. 24, 500 B. 22, 000C. 20, 500 D. 19, 000SITAMS Page 17

REASONING COURSEPie Charts & Line GraphsSolutions for exercise problems:1. Answer: (A)Total percentage = (10 / 24) x 100 = 41.6666667 %2. Answer: (D)20 + 10 = 30% is made up of either bones or skin. Hence, 70% is made up of neither.3. Answer: (D)It cannot be determined since the respective distributions are not known.4. Answer: (D)Although it seems to be Commodore, the answer cannot be determined due to the fact that weare unaware of the break-up of the sales value and volume of companies compromising theother categories.5. Answer: (A)If we assume the total sales to be 100 in the first year, IBM's sales would go up by 50% (from28 to 42) contributing an increase of 14 to the total sales value.Similarly, Apple's increase of 15% would contribute an increase of 2.1 to the total salesvalue. The net change would be 14 + 2.1 on 100. (i.e., 16.1%)6. Answer: (D)IBM accounts for 28% of the share by value and 10% of the share by volume.28% of 1650000 = 28 x 1650000/100 = 46200010% of 1500 = 10 x 1500/100 = 150Therefore, average unit sale price = 462000/150 = 3080.7. Answer: (B)20% of the total funds to be arranged = Rs. (20% of 57600) crores= Rs. 11520 croresRs. 11486 crores.Rs. 11486 crores is the amount of funds to be arranged through External Assistance.8. Answer: (C)Shortage of funds arranged = Rs. (11486 - 9695) croresthrough External Assistance= Rs. 1791 crores.Increase required in Market Borrowing = Rs. 1791 crores.1791Percentage increase required = x 100 % = 5.98% 6%.299529. Answer: (C)Amount permitted10. Answer: (C)= (Funds required from Toll for projects of Phase II) + (10% ofthese funds)= Rs. 4910 crores + Rs. (10% of 4910) crores= Rs. (4910 + 491) crores= Rs. 5401 crores.Central angle corresponding to Market Borrowing = 29952 x 360º = 187.2º5760011. Answer: (B)Required ratio = 4910 = 1 1 .29952 6.1 612. Answer: (A)Percentage of money spend on Tennis =45 x 100 % = 121360 2SITAMS Page 18

REASONING COURSEPie Charts & Line Graphs13. Answer: (D)Let the total spending on sports be Rs. x. Then,36 xAmount spent on Golf = Rs. x x = Rs. .360 1063 7xAmount spent on Hockey = Rs x x = Rs. .360 407x xDifference = Rs. - = Rs 3x .40 10 40Required percentage = Rs.3x/40x 100 % = 75%.x/1014. Answer: (A)Amount spent on Basketball exceeds that on Tennis by:Rs. [ (50 - 45) x 1,80,00,000] = Rs. 2, 50,000.36015. Answer: (C)Let the total spending on sports be Rs. x. Then,81 9x x x = Rs. .Amount spent on Cricket = Rs. 360 4054 3xAmount spent on Football = Rs x x = Rs. .360 209x 3xDifference = Rs. - = Rs 3x .40 20 403x/40Required percentage = Rs.x 100 % = 33 1 %.9x/40 316. Answer: (C)Let the amount of Royalty to be paid for these books be Rs. r.30600 x 15Then, 20 : 15 = 30600 : r r = Rs.= Rs. 22,950.2017. Answer: (C)Central angle corresponding to Royalty = (15% of 360)º=15 x 360º100= 54º.18. Answer: (B)Clearly, marked price of the book = 120% of C.P.Also, cost of paper = 25% of C.PLet the cost of paper for a single book be Rs. n.Then, 120 : 25 = 180 : nn = Rs.25 x 180 = Rs. 37.50 .12019. Answer: (A)For the publisher to earn a profit of 25%, S.P. = 125% of C.P.Also Transportation Cost = 10% of C.P.SITAMS Page 19

REASONING COURSEPie Charts & Line GraphsLet the S.P. of 5500 books be Rs. x.Then, 10 : 125 = 82500 : xx = Rs.125 x 8250010= Rs. 1031250.S.P. of one book = Rs.10312505500= Rs. 187.50 .20. Answer: (D)Printing Cost of book = 20% of C.P.Royalty on book = 15% of C.P.Difference = (20% of C.P.) - (15% of C.P) = 5% of C.P.Percentage difference =DifferencePrintingCostx100 %21. Answer: (D)Central angle of 18º 18 x100 % of the total expenditure= 360= 5% of the total expenditure.From the given chart it is clear that:=5% of C.P.PrintingCostOut of the given combinations, only in combination (d) the difference is 5% i.e.Paper Cost - Printing Cost = (25% - 20%) of the total expenditure= 5% of the total expenditure.22. Answer: (B)Clearly, S.P. of the book = 105% of C.P.Clearly, S.P. of the book = 105% of C.P.Then, 15 : 105 = 281250 : xx = Rs.105 x 281250 = Rs. 1968750.15x100 % = 25%.S.P. of one book = Rs.1968750 = Rs. 157.50 .1250023. Answer: (B)Let the Promotion Cost for this edition be Rs. p.Then, 25 : 10 = 56250 : p24. Answer: (A)Central angle of 108º == 30% of the total expenditure.From the pie chart it is clear that:Binding Cost + Transportation Costp = Rs.56250 x 10 = Rs. 22,500.25108 x 100 % of the total expenditure360= (20% + 10%) of the total expenditure= 30% of the total expenditure.Binding Cost and Transportation Cost together have a central angle of 108º.SITAMS Page 20

REASONING COURSEPie Charts & Line Graphs25. Answer: (D)Central angle corresponding to Royalty = (10% of 360)º=10 x 360º100= 36º.26. Answer: (D)Total exports of the three Companies X, Y and Z together, during various years are:In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores.In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores.In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores.In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores.In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores.In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores.In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores.Clearly, the total exports of the three Companies X, Y and Z together are same during theyears 1995 and 1996.27. Answer: (D)1. The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995,1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.2. The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995,1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.3. The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995,1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.Average annual exports (in Rs. crore) of Company Y during the given period= 1 x (80 + 40 + 60 + 60 + 80 + 100 + 140) = 560 = 80.7 7Average annual exports (in Rs. crore) of Company Z during the given period= 1 x (60 + 90 + 120 + 90 + 60 + 80 + 100) = 600 .7 780Required percentage =600x 100 % 93.33%.728. Answer: (C)The difference between the exports from the Companies X and Y during the various yearsare:In 1993 = Rs. (80 - 30) crores = Rs. 50 crores.In 1994 = Rs. (60 - 40) crores = Rs. 20 crores.In 1995 = Rs. (60 - 40) crores = Rs. 20 crores.In 1996 = Rs. (70 - 60) crores = Rs. 10 crores.In 1997 = Rs. (100 - 80) crores = Rs. 20 crores.In 1998 = Rs. (100 - 50) crores = Rs. 50 crores.In 1999 = Rs. (140 - 120) crores = Rs. 20 crores.Clearly, the difference is minimum in the year 1996.29. Answer: (C)Average exports of the three Companies X, Y and Z in 1993= Rs. 1 x (30 + 80 + 60) crores = Rs. 170 crores.SITAMS Page 21

REASONING COURSEPie Charts & Line Graphs3 3Average exports of the three Companies X, Y and Z in 19981 230= Rs. x (50 + 100 + 80) crores = Rs. crores.3 3230 170Difference = Rs. - crores3 3= Rs.60 crores3= Rs. 20 crores.30. Answer: (C)Average annual exports of Company Z during the given period= 1 x (60 + 90 + 120 + 90 + 60 + 80 + 100)7600= Rs. crores7= Rs. 85.71 crores.From the analysis of graph the exports of Company Z are more than the average annualexports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995, 1996 and 1999,i.e., during 4 of the given years.31. Answer: (D)The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.Let the exports in the year 1998 = Rs. x crores.Then, the exports in the year 1999 = Rs. (500 - x) crores.1.25 = 250 x = 250 = 200 [Using ratio for 1998]x 1.25Thus, the exports in the year 1999 = Rs. (500 - 200) crores = Rs. 300 crores.Let the imports in the year 1999 = Rs. y crores.Then, 1.40 = y y = (300 x 1.40) = 420.300Imports in the year 1999 = Rs. 420 crores.32. Answer: (C)The imports are minimum proportionate to the exports implies that the ratio of the value ofimports to exports has the minimum value.Now, this ratio has a minimum value 0.35 in 1997, i.e., the imports are minimumproportionate to the exports in 1997.33. Answer: (D)The graph gives only the ratio of imports to exports for different years. To find thepercentage increase in imports from 1997 to 1998, we require more details such as the valueof imports or exports during these years.Hence, the data is inadequate to answer this question.34. Answer: (B)Ratio of imports to exports in the year 1996 = 0.85.Let the exports in 1996 = Rs. x crores.SITAMS Page 22

REASONING COURSEPie Charts & Line GraphsThen, 272 = 0.85 x = 272 = 320.x 0.85Exports in 1996 = Rs. 320 crores.35. Answer: (D)The exports are more than the imports imply that the ratio of value of imports to exports isless than 1.Now, this ratio is less than 1 in years 1995, 1996, 1997 and 2000.Thus, there are four such years.36. Answer: (D)Required difference = (128000 - 107000) = 21000.37. Answer: (C)From the line-graph it is clear that the productions of Company X in the years 1997, 1998,1999, 2000, 2001 and 2002 are 119000, 99000, 141000, 78000, 120000 and 159000 andthose of Company Y are 139000, 120000,100000, 128000, 107000 and 148000 respectively.Total production of Company X from 1997 to 2002= 119000 + 99000 + 141000 + 78000 + 120000 + 159000= 716000.and total production of Company Y from 1997 to 2002= 139000 + 120000 + 100000 + 128000 + 107000 + 148000= 742000.Difference = (742000 - 716000) = 26000.38. Answer: (A)Average number of vehicles manufactured by Company X= 1 x (119000 + 99000 + 141000 + 78000 + 120000 + 159000)6= 119333.39. Answer: (D)The difference between the productions of Companies X and Y in various years is:For 1997 (139000 - 119000) = 20000.For 1998 (120000 - 99000) = 21000.For 1999 (141000 - 100000) = 41000.For 2000 (128000 - 78000) = 50000.For 2001 (120000 - 107000) = 13000.For 2002 (159000 - 148000) = 11000.Clearly, maximum difference was in 2000.40. Answer: (B)Required percentage = 128000 x 100 % 164%.7800041. Answer: (C)Let the incomes in 2000 of Companies X and Y be 3x and 4x respectively.And let the expenditures in 2000 of Companies X and Y be E 1 and E 2 respectively.Then, for Company X we have:65 = 3x - E 1x 10065 =3x - 1 E1 = 3x x 100 .... (i)E 1 100 E 1 165For Company Y we have:50 = 4x - E 2x 10050 =4x - 1 E2 = 4x x 100 .... (ii)E 2 100 E 2 150SITAMS Page 23

REASONING COURSEPie Charts & Line GraphsFrom (i) and (ii), we get:3x x 100E 1 165 3 x 150 15 = = = (Required ratio).E 24x x 100 4 x 165 2215042. Answer: (B)Profit percent of Company Y in 1997 = 35.Let the income of Company Y in 1997 be Rs. x crores.Then, 35 = x - 220 x 100 x = 297.220Income of Company Y in 1997 = Rs. 297 crores.43. Answer: (D)Let the expenditures of each companies X and Y in 1996 be Rs. x crores.And let the income of Company X in 1996 be Rs. z crores.So that the income of Company Y in 1996 = Rs. (342 - z) crores.Then, for Company X we have:40 = z - x 40 z 100zx 100= - 1 x = .... (i)x 100 x 140Also, for Company Y we have:45 = (342 - z) 45 (342 - z) (342 - z) x 100x 100 = - 1 x = .... (ii)x 100 x 145From (i) and (ii), we get:100z (342 - z) x 100= z = 168.140 145Substituting z = 168 in (i), we get : x = 120.Total expenditure of Companies X and Y in 1996 = 2x = Rs. 240 crores.Total income of Companies X and Y in 1996 = Rs. 342 crores.Total profit = Rs. (342 - 240) crores = Rs. 102 crores.44. Answer: (A)Let the income of Company X in 1998 be Rs. x crores.Then, 55 = x - 200 x 100 x = 310.200Expenditure of Company X in 2001 = Income of Company X in 1998= Rs. 310 crores.Let the income of Company X in 2001 be Rs. z crores.Then, 50 = z - 310 x 100 z = 465.310Income of Company X in 2001 = Rs. 465 crores.45. Answer: (D)Let the incomes of each of the two Companies X and Y in 1999 be Rs. x.And let the expenditures of Companies X and Y in 1999 be E 1 and E 2 respectively.Then, for Company X we have:50 = x - E 1 50 xx 100 = - 1 x = 150 E 1 .... (i)E 1 100 E 1 100SITAMS Page 24

REASONING COURSEPie Charts & Line GraphsAlso, for Company Y we have:60 = x - E 2 60 xx 100 = - 1 x = 160 E 2 .... (ii)E 2 100 E 2 10046. Answer: (B)The differences between the percentages of candidates qualified to appeared for the give pairsof years are:For 1994 and 1995 = 50 - 30 = 20.For 1998 and 1999 = 80 - 80 = 0.For 1994 and 1997 = 50 - 30 = 20.For 1997 and 1998 = 80 - 50 = 30.For 1999 and 2000 = 80 - 60 = 20.Thus, the maximum difference is between the years 1997 and 1998.47. Answer: (D)The graph gives the data for the percentage of candidates qualified to appeared and unless theabsolute values of number of candidates qualified or candidates appeared is know we cannotcompare the absolute values for any two years.Hence, the data is inadequate to solve this question.48. Answer: (C)The number of candidates appeared in 1998 be x.Then, 80% of x = 21200 x = 21200 x 100 = 26500 (required number).8049. Answer: (D)The total number of candidates qualified in 1996 and 1997 together, cannot be determineduntil we know at least, the number of candidates appeared in any one of the two years 1996or 1997 or the percentage of candidates qualified to appeared in 1996 and 1997 together.Hence, the data is inadequate.50. Answer: (C)The number of candidates qualified in 1999 = (80% of 26500) = 21200.Number of candidates qualified in 2000 = ( 33500 - 21200 ) = 12300.Let the number of candidates appeared in 2000 be x.Then, 60% of x = 12300 x = 12300 x 100 = 20500.60SITAMS Page 25

REASONING COURSEPie Charts & Line GraphsQUESTION BANK FOR MOCKTESTSITAMS Page 26

REASONING COURSEPie Charts & Line GraphsPIE CHARTS:QUESTION 1-4Study the following pie-chart and the table and answer the questions based on them.Proportion of Population of Seven Villages in 1997Village% Population Below Poverty LineX 38Y 52Z 42R 51S 49T 46V 581. If the population of village R in 1997 is 32000, then what will be the population of villageY below poverty line in that year?A. 14100 B. 15600C. 16500 D. 170002. The ratio of population of village T below poverty line to that of village Z below povertyline in 1997 is:A.11:23 B. 13:11C. 23:11 D. 11:133. Find the population of village S if the population of village X below poverty line in 1997 is12160.A. 18, 500 B. 20, 500C. 22, 000 D. 26, 0004. If in 1998, the population of villages Y and V increase by 10% each and the percentage ofpopulation below poverty line remains unchanged for all the villages, then find the populationof village V below poverty line in 1998, given that the population of village in 1997 was30000.A. 11, 250 B. 12, 760C. 13, 140 D. 13, 780QUESTION 5-10The following pie chart shows the amount of subscriptions generated for India Bonds fromdifferent categories of investors.SITAMS Page 27

REASONING COURSEPie Charts & Line GraphsSubscriptions Generated for India Bonds5. In the corporate sector, approximately how many degrees should be there in the centralangle ?A. 120 B. 121C. 122 D. 1236. If the investment by NRI's are Rs 4,000 crore, then the investments by corporate housesand FII's together is:A. 24, 000 crore B. 24, 363 croreC. 25, 423 crore D. 25, 643 crore7. What percentage of the total investment is coming from FII's and NRI's ?A. 33 % B. 11 %C. 44 % D. 22 %8. If the total investment other than by FII and corporate houses is Rs 335,000 crore, then theinvestment by NRI's and Offshore funds will be (approximately) ?A. 27, 4100 B. 28, 5600C. 29, 300 D. Cannot be determined9. If the total investment flows from FII's were to be doubled in the next year and theinvestment flows from all other sources had remained constant at their existing levels for thisyear, then what would be the proportion of FII investment in the total investment into IndiaBonds next year (in US $ millions) ?A. 40 % B. 50 %C. 60 % D. 70 %10. What is the approximate ratio of investment flows into India Bonds from NRI's tocorporate houses?A.1:4 B. 1:3C. 3:1 D. cannot be determinedQUESTION 11-15Study the following pie-diagrams carefully and answer the questions given below it:Percentage Composition of Human BodySITAMS Page 28

REASONING COURSEPie Charts & Line Graphs11. What percent of the total weight of human body is equivalent to the weight of the proteinsin skin in human body?A. 0.016 % B. 1.6 %C. 0.16 % D. Data inadequate12. What will be the quantity of water in the body of a person weighing 50 kg?A. 25 Kg B. 35 KgC. 41 Kg D. 42.5 Kg13. What is the ratio of the distribution of proteins in the muscles to that of the distribution ofproteins in the bones?A.1:18 B. 1:2C. 2:1 D. 18:114. To show the distribution of proteins and other dry elements in the human body, the arc ofthe circle should subtend at the centre an angle of:A.54° B. 126°C. 108° D. 252°15. In the human body, what part is made of neither bones nor skin?A.1/40 B. 2/80C. 3/5 D. None of theseQUESTIONS 16-20Study the following graph and the table and answer the questions given below.Data of different states regarding population of states in the year 1998SITAMS Page 29

REASONING COURSEPie Charts & Line GraphsTotal population of the given States = 3276000.Sex and Literacy wise Population RatioStatesSexLiteracyM F Literate IlliterateA.P 5 3 2 7M.P 3 1 1 4Delhi 2 3 2 1Goa 3 5 3 2Bihar 3 4 4 1U.P. 3 2 7 2T.N. 3 4 9 416. What will be the percentage of total number of males in U.P., M.P. and Goa together tothe total population of all the given states?A. 25 % B. 27.5 %C. 28.5 % D. 31.5 %17. What was the total number of illiterate people in A.P. and M.P. in 1998?A. 8, 76, 040 B. 9, 32,170C. 9, 81, 550 D. 11, 61, 16018. What is the ratio of the number of females in T.N. to the number of females in Delhi?A.7:5 B. 9:7C. 13:11 D. 15:1419. What was the number of males in U.P. in the year 1998?A. 2, 54, 650 B. 2, 94,840C. 3, 21, 470 D. 3, 41, 20020. If in the year 1998, there was an increase of 10% in the population of U.P. and 12% in thepopulation of M.P. compared to the previous year, and then what was the ratio of populationsof U.P. and M.P. in 1997?A.42:55 B. 48:55C. 7:11 D. 4:5QUESTIONS 20-25The circle graph given here shows the spending of a country on various sports during aparticular year. Study the graph carefully and answer the questions given below it.SITAMS Page 30

REASONING COURSEPie Charts & Line Graphs1 Golf 36°2 Tennis 45°3 Basketball 50°4 Cricket 81°5 Hockey 63°6 Football 54°7 Others 31°21. What percent of the total spending is spent on Tennis?A. 12 1/2 % B. 22 1/2 %C. 45% D. 25 %22. How much percent more is spent on Hockey than that of Golf?A. 27 % B. 35 %C. 37.5 % D. 75 %23. How much percent less is spent on Football than that on Cricket?A. 22 2/9 % B. 27 %C. 37 1/2 % D. 33 1/3 %24. If the total amount spent on sports during the year was Rs. 2 crores, the amount spent onCricket and Hockey together was:A. Rs. 8, 00, 000 B. Rs. 80, 00, 000C. Rs. 1, 20, 00, 000 D. Rs. 1, 60, 00, 00025. If the total amount spent on sports during the year be Rs. 1, 80, 00, 000, the amount spenton Basketball exceeds that on Tennis by:A. Rs. 82, 50, 000 B. Rs. 3, 60, 000C. Rs. 3, 75, 000 D. Rs. 4, 10, 000LINE GRAPHS:QUESTIONS 26-30Answer the questions based on the given line graph. [R.B.I. 2003]Ratio of Exports to Imports (in terms of money in Rs. crores) of Two Companies Overthe Years26. In how many of the given years were the exports more than the imports for Company A?SITAMS Page 31

REASONING COURSEPie Charts & Line GraphsA. 2 B. 3C .4 D. 527. If the imports of Company A in 1997 were increased by 40 percent, what would be theratio of exports to the increased imports?A. 1.20 B. 1.25C. 1.30 D. cannot be determined28. If the exports of Company A in 1998 were Rs. 237 crores, what was the amount ofimports in that year?A. Rs. 189.6 crore B. Rs. 243 croreC. Rs. 281 crore D. Rs. 316 crore29. In 1995, the export of Company A was double that of Company B. If the imports ofCompany A during the year was Rs. 180 crores, what was the approximate amount of importsof Company B during that year?A. Rs. 190 crore B. Rs. 210 croreC. Rs. 225 crore D. Cannot be determined30. In which year(s) was the difference between impors and exports of Company B themaximum?A. 2000 B. 1996C. 1998 & 2000 D. Cannot be determinedQUESTIONS 31-35Study the following line graph which gives the number of students who joined and left theschool in the beginning of year for six years, from 1996 to 2001. [S.B.I. P.O. 2001]Initial Strength of school in 1995 = 3000.31. The number of students studying in the school during 1999 was?A. 2950 B. 3000C. 3100 D. 315032. For which year, the percentage rise/fall in the number of students who left the schoolcompared to the previous year is maximum?A. 1997 B. 1998C. 1999 D. 2000SITAMS Page 32

REASONING COURSEPie Charts & Line Graphs33. The strength of school increased/decreased from 1997 to 1998 by approximately whatpercent?A. 1.2 % B. 1.7 %C. 2.1 % D. 2.4 %34. The number of students studying in the school in 1998 was what percent of the number ofstudents studying in the school in 2001?A. 92.13 % B. 93.75 %C. 96.88 % D. 97.25 %35. The ratio of the least number of students who joined the school to the maximum numberof students who left the school in any of the years during the given period is?A. 7:9 B. 4:5C. 3:4 D. 2:3QUESTIONS 36-40In a school the periodical examination are held every second month. In a session duringApril 2001 - March 2002, a student of Class IX appeared for each of the periodicalexams. The aggregate marks obtained by him in each periodical exam are represented inthe line-graph given below. [S.B.I. P.O. 2003]Marks Obtained by student in Six Periodical Held in Every Two Months Duringthe Year in the Session 2001 - 2002.Maximum Total Marks in each Periodical Exam = 50036. In which periodical exams did the student obtain the highest percentage increase in marksover the previous periodical exams?A. June, 01 B. August, 01C. Oct, 01 D. Dec, 0137. The total number of marks obtained in Feb. 02 is what percent of the total marks obtainedin April 01?A. 110 % B. 112.5 %C. 115 % D. 116.5 %38. What is the percentage of marks obtained by the student in the periodical exams ofAugust, 01 and Oct, 01 taken together?A. 73.25 % B. 75.5 %C. 77 % D. 78.75 %39. What are the average marks obtained by the student in all the periodical exams during thelast session?A. 373 B. 379C. 381 D. 385SITAMS Page 33

REASONING COURSEPie Charts & Line Graphs40. In which periodical exams there is a fall in percentage of marks as compared to theprevious periodical exams?A. None B. June, 01C. Oct, 01 D. Feb, 02QUESTIONS 41-43:Velocity-time graphConsider the motion of the object whose velocity-time graph is given in the diagram.41. What is the acceleration of the object between times t=0 and t=2?A. 4 m/s² B. 6 m/s²C. -4 m/s² D. -6 m/s²42. What is the acceleration of the object between times t=0 and t=12?A. 2 m/s² B. -2 m/s²C. 4 m/s² D. -4 m/s²43. What is the net displacement of the object between times t=0 and t=16?A. 200m B. 400mC. 100m D. 50mQUESTIONS 44-50Study the following line graphs which gives the number of students who joined and left theschool in beginning of year for six years, from 1-6.Initial strength of school in 1995 = 3000The questions given below the graph are based on this line graphsSITAMS Page 34

REASONING COURSEPie Charts & Line Graphs44. The strength of the school increased/decreased from 2-3 year by approximately whatpercent?A. 1.2 % B. 1.7 %C. 2.1 % D. 2.4 %45. The number of students studying in the school during 4 th year?A. 2950 B. 3000C. 3100 D. 315046. During which of the following pairs of years, the strength of the school was same?A. 4 & 6 B. 5 & 3C. 2 & 3 D. 1 & 547. The number of students studying in the school in 3 rd year was what percent of number ofstudents studying in the school in 7 th year?A. 92.13 % B. 93.75 %C. 96.88 % D. 97.2548. Among the given years, the largest number of students joined the school in the year:A. 1 B. 3C. 4 D. 749. For which year, the percentage rise/fall in the number of students who left the schoolcompared to the previous year is maximum?A. 2 B. 3C. 4 D. 550. The ratio of the least number of students who joined the school to the maximum numberof students who left the school in any of the years during the given period?A. 7:9 B. 4:5C. 3:4 D. 2:3SITAMS Page 35

REASONING COURSEPie Charts & Line GraphsAnswers for Mock Test :1.B 2.C 3.C 4.B 5.C6.B 7.C 8.A 9.B 10.B11.B 12.B 13.C 14.C 15.D16.C 17.D 18.D 19.B 20.A21.A 22.D 23.C 24.B 25.A26.B 27.B 28.D 29.B 30.D31.D 32.A 33.B 34.B 35.D36.C 37.B 38.B 39.C 40.A41.A 42.B 43.C 44.B 45.D46.D 47B. 48.D 49.A 50.DSITAMS Page 36