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Practice Exercise 3

Directions (Q. 1-5): Refer to the pie-charts below and answer the questions that follow.Monthly income and expenditure for a semi-government institute

INCOME

Government35%

Ins titute25%

Students40%

EXPENDITURE

Awards5%

Renovation 9%

Wages55%

Facilities31%

There are some constraints:i) Income from students can be used for awards and facilities; otherwise it has to be kept aside.ii) Renovation can be done only with donation from institute.iii) Government and institute’s contributions do not increase even if any new course is intro-

duced for/till first 2 years.

1. If government’s contribution was Rs 10 lakh and the management could save Rs 60000, thenwhat would be the expenditure on wages? (approximately)1) Rs 1504000 2) Rs 1538000 3) Rs 1602000 4) Rs 1571000

2. The total income is Rs 35 × 106. The percentage utilization of the income from the students is100%. If expenditure on awards and facilities is met only with income from students, then what isthe total expenditure? (approximately)1) Rs 31.5 × 106 2) Rs 35 × 106

3) Rs 39 × 106 4) Rs 40 × 106

3. Approximately what is the ratio of the expenditure on facilities to that on wages?1) 5 : 11 2) 11 : 63) 6 : 11 4) Cannot be determined

4. If no money is spent on renovation then the income and the expenditure are the same, otherwisethere is a shortage of Rs 650000. Then what is the total income?1) Rs 72 × 105 2) Rs 65.7 × 105 3) Rs 59.5 × 105 4) Rs 54.5 × 105

5. Students’ contribution is totally used in awards and facilities but Rs 6102 is still left. Find thetotal expenditure (in Rs).

1) 6105 2) 6105.7 3) 4×106 4) Data inadequateDirections (Q. 6-10): Refer to the bar graph below and answer the questions that follow.

In the game of basketball, points for the correct throws are 1, 2 or 3. In a match the number ofattempts to basket the ball and accuracy are given for all players of the team below. Indian Railways’players are A, B, C, D and E.

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20

40

60

80

100

5

10

15

20

25

1-pointer attempts (%)

B C D E

2-pointer attempts (%)

3-pointer attempts (%) Total number of attempts

A

PlayerAccuracy

1-pointer 2-pointer 3-pointer

A 66.66 33.33 20

B 100 66.66 100

C 75 75 100

D 88.88 100 50

E 100 71.42 83.33

6. How many points were scored by player A?1) 13 2) 19 3) 21 4) 39

7. What was the accuracy of the most accurate player? (Accuracy means no. of baskets per attempt.)1) 78% 2) 80%3) 83% 4) 87%

8. What percentage of total points was scored by player D?1) 13% 2) 21% 3) 30% 4) 37%

9. What percentage of total points was scored through 2-pointers?1) 22% 2) 32% 3) 42% 4) 52%

10. Point scored by all players from 3-pointers is what percentage (approx.) more/less than those from2-pointers?1) 15% more 2) 10% less3) 15% less 4) 10% more

Directions (Q. 11-15): Refer to the graphs below and answer the questions that follow.Graph (i) shows volumewise share of various companies in car market in India, for March 2004.Graph (ii) shows total number of cars sold since October 2003 to March 2004.Graph (iii) shows ratios of market prices of cars of the companies which are written next to each

other, ie price of Bajaj car

price of Toyota car

= 0.66

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Graph (i)Bajaj

Honda

Toyota

Maruti

M&M

Graph (ii) Graph (iii)Number of cars sold (in thousands)

0

10

20

30

40

50

60

70

80

Oct2003

Nov2003

Dec2003

Jan2004

Feb2004

Mar2004

0.66 0.625

2

1.1

00

0.5

1

1.5

2

2.5

Toyota Bajaj Maruti Honda M&M

11. What is the share of M&M in total sale (in Rs) of cars in March 2004?1) 32% 2) 48% 3) 60% 4) Cannot be determined

12. If Toyota had 20% share in volume in November 2003, then what is the ratio of its sales (units) inNovember 2003 to that in March 2004?1) 11 : 10 2) 8 : 5 3) 44 : 25 4) None of these

13. If a Honda car costs Rs 2.5 lakhs, then what were the sales of Bajaj cars in March 2004?1) Rs 125 crores 2) Rs 160 crores 3) Rs 250 crores 4) Rs 300 crores

14. How many cars cost more than the average price of cars in March 2004 among the given group ofcars?1) 1 2) 2 3) 3 4) Cannot be determined

15. If the cost of Bajaj car is Rs 108000 less than that of M&M, then the income from the selling of acar by Maruti is what % more/less than that by Honda in March 2004?1) 60% less 2) 50% less 3) 40% more 4) 25% lessDirections (Q. 16-20): The following table shows the percentage population above poverty line

and ratio of male to female above and below poverty line for states A, B, C, D and E in year 2003.

Name of State % population abovepoverty line

Ratio of male to female

Below poverty line Above poverty line

A 72 4 : 3 4 : 5

B 64 8 : 10 9 : 7

C 56 6 : 5 13 : 15

D 84 7 : 9 11 : 10

E 76 5 : 7 9 : 10

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16. In which state is the maximum male population below poverty line?1) C 2) B3) A 4) Can’t be determined

17. If the female population below poverty line in state D is 6.3 million, find the female populationabove poverty line.1) 38 million2) 28 million3) 40 million4) 42 million

18. If the female population above poverty line in state A is 3.6 million more than the female popula-tion above poverty line in state D, find the difference between total population of State A and stateD.1) 9 million2) 8 million3) 10 million4) Can’t say

19. If the percentage of male population below poverty line in state C and state E together is 15%, findthe % male population above poverty line in states C and E together.1) 45.2% 2) 32.4% 3) 37.8% 4) Can’t say

20. If the female population above poverty line in state C is greater than the female population abovepoverty line in state B, which of the following is definitely true?1) Population of state C < population of state B2) Population of state C > population at state B3) Population of state C = population of state B4) Can’t say

Answers and explanations1. 2; Government’s contribution = 35% of the total income

Total income = 285714335

100106

Savings = Rs 60000 Total expenditure = Total income - savings = 2857143 - 60000 = 2797143.Expenditure on wages = 55% of total expenditure 1538429.

2. 3; From condition (i), 100% income from students is utilized. income from students = expenditure on awards and facilities. 40% of income = 36% of expenditure.

Expenditure = 66 10393900000388889103510040

36100

3. 3; Facilities-to-wages ratio = 31

55

6

11

4. 2; From the given information, total income = total expenditure - 9% of total expenditure = total expenditure - 650000

= 657000065722226500006500009

100

5. 4; Let the total income be Rs x and total expenditure be Rs y.According to the question,

40% of x – 36% of y = 5102But we can’t find the value of y.Hence, data inadequate.

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6-9:

PlayerNo. of attempts for

1-pointer 2-pointer 3-pointer

A 6 9 5

B 3 6 1

C 8 4 3

D 9 3 6

E 4 14 6

Total 30 36 21

PlayerNumber of baskets

1-pointer 2-pointer 3-pointer

A 4 3 1

B 3 4 1

C 6 3 3

D 8 3 3

E 4 10 5

Total 25 23 13

6. 1; Points scored by player A = 4 × 1 + 3 × 2 + 1 × 3 = 4 + 6 + 3 = 13Alternatively:Player A has overall accuracy of around 40% with quite a low accuracy of 3 pointers.With total 20 attempts, assuming average score of 2 per attempt, approximate score would be0.4 × 2 × 20 = 16.

7. 2;

Player A B C D E

Accuracy 8/20 = 0.4 8/10 = 0.8 12/15 = 0.8 14/18 < 0.8 19/24 < 0.8

Players B and C have the maximum accuracy of 80%.8. 2; Total points = 25 × 1 + 23 × 2 + 13 × 3 = 25 + 46 + 39 = 110

Points scored by player D = 8 × 1 + 3 × 2 + 3 × 3 = 23

Percentage of points scored by player D = %2110011023

Alternatively:Approximately 20% of total attempts were made by player D with the same accuracy (approxi-mately) as the other players except A, whose accuracy is quite low. Hence, player D must havescored approximately 20% of total points.

9. 3; Number of points scored through 2-pointers = 2 × 23 = 46

Percentage of points through 2-pointers = %4210011046

.

10. 3; Total points scored from 3-pointers = 13 × 3 = 39Total points scored from 2-pointers = 23 × 2 = 46

Required percentage = %2.1510046

3946

11. 1; From graph (iii)Price of Bajaj

Price of Toyota

2

3 ; Price of Maruti

Price of Bajaj

5

8 ;Price of Honda

Price of Maruti 2; 1.1

Honda of PriceM&M of Price

If price of Bajaj car is 8x, then prices of Toyota, Maruti, Honda and M&M cars are 12x, 5x, 10xand 11x respectively.From graph (i),

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Percentage shares of Honda and Toyota are 12.5% each while those of Bajaj, M&M and Marutiare 25% each.

Sales of M&M cars (in value) in 2004 = 1125

10050000x

Total sales (in value) = (8x + 11x + 5x) × 25

100 × 50000 + (12x + 10x) ×

125

10050000

.

= (24x + 11x) × 25

100 × 50000 = 35x ×

25

100 × 50000

Percentage share of sales of M&M cars = %321003511

12. 3; Sales of Toyota in November 2003

Sales of Toyota in March 2004

20

10055

125

10050

220

125

44

25.

13. 3; If a Honda car costs Rs 2.5 lakhs, then a Bajaj car will cost 625.025.2 Rs 2 lakhs.

Sales of Bajaj cars in March 2004 = 25

10050000 2 = 25000 lakhs.

14. 3; Ratio of price of all the given companies isToyoto : Bajaj : Maruti : Honda : M & M

3 : 28 : 5

1 : 2 10 : 11

11252:10252:10152:10182:10183

11:10:5:8:12220:200:100:160:240 Volumes of production of Toyota, Bajaj, Maruti, Honda and M&M in March 2004 are in the ratio1 : 2 : 2 : 1 : 2Let x be present in the ratio of the price of each of the cars.

Average price in March 2004 = xxxxxxx 75.88

7021221

2111102528112

Therefore the prices of Toyota, Honda and M&M are greater than the average price of all cars inMarch 2004.

15. 2; From solution (11) : Ratio of market prices is Bajaj : M&M = 8x : 11x 11x – 8x = 3x = 1,08,000 x = 36,000Now market price of Maruti = 5x = 180,000Market price of Honda = 10x = 3,60,000 required answer = 50%.Quicker Approach:Ratio of price of Honda to Maruti = 2 : 1

Required ratio = %501002

12

Note: There is no need of the cost of Bajaj car in March 2004.16. 4; Total population of each of the states is not given. Hence data inadequate.

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17. 2; 169

part of 16% 6.3 million

9% 6.3 milion

2110

part of 84% ie 40% 284093.6

million.

18. 1; At first glance, data seems inadequate for the question.Let total population of state A and state D be x and y respectively.

Female population above poverty line in state A = 95

part of 72% of x = 40% of x.

Female population above poverty line in state D = 2110

part of 84% of y = 40% of y.

According to the question,40% of x – 40% of y = 3.6 40% of 6.3 yx yx = 9 millionNote: If percentages are different then we can’t solve the problem.

19. 2; Percentage male population below poverty line in state C = 116

part of 44% = 24%

and that in state E = 125

part of 24% = 10%

Combining both states, we have 15% male population below poverty line.It means that 15% is the weighted mean of 10% and 24%.C E24% 10%

15%5 9Therefore, total populations of C and E are in the ratio 5 : 9.

Now, % male population above poverty line in state C = 2813

part of 56% = 26%

and that in state E = 199

part of 76% = 36%.

Required % = %4.3214454

14324130

95936526

20. 4; Let the total population of state C and state B be x and y respectively.According to the question,

2815

part of 56% of x > 167

part of 64% of y

30% of x > 28% of y x > y or x < y or x = y.