Exercise 3


1. Naresh’s monthly income is 30% more than that of Raghu. Raghu’s monthly income is 20% less than that of Vishal. If the difference between the monthly incomes of Naresh and Vishal is 800, what is the monthly income of Raghu?
(a) 16,000
(b) 20,000
(c) 12,000
(d) Data inadequate
(e) None of these
Ans.a

N = R + 30% of R = 1.3 RR

= V – 20% of V = 80% of V = 0.8 V

∴ N = 1.3 × 0.8V = 1.04 V

Now, N – V = 1.04 V – V = 0.04 V = ₹ 800(given)

∴ V = ₹ 20000

∴ R = 0.8 × 20000 = ₹ 16000

2. In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 5% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
(a) 4 : 5
(b) 5 : 4
(c) 2 : 3
(d) Data inadequate
(e) None of these
Ans.a

Let the population of males = x; then the population of females = 9000 – x

Now, 5% of x + 8% of (9000 – x)

= (9600 – 9000 ) = 600

or 0.05x + 720 – 0.08x = 600

or 720 – 600 = 0.08x – 0.05x

or, 120 = 0.03x

x = 4000

Reqd ratio of population of males and females

\(\frac{4000}{9000 - 4000} = \frac{4000}{5000} = 4 : 5\)
3. A petrol pump owner mixed leaded and unleaded petrol in such a way that the mixture contains 10% unleaded petrol. What quantity of leaded petrol should be added to 1 ltr mixture so that the percentage of unleaded petrol becomes 5%?
(a) 1000 ml
(b) 900 ml
(c) 1900 ml
(d) 1800 ml
(e) None of these
Ans.a

In 1 lit mixture quantity of unleaded petrol = 100 ml

Let x ml leaded petrol be added, then

5% of (1000 + x) = 100 ml

or, 5 (1000 + x) = 100 × 100

⇒ x = 50005 = 1000 ml

4. Out of a total 85 children playing badminton or table tennis or both, total number of girls in the group is 70% of the total number of boys in the group. The number of boys playing only badminton is 50% of the number of boys and the total number of boys playing badminton is 60% of the total number of boys. The number of children playing only table tennis is 40% of the total number of children and a total of 12 children play badminton and table tennis both. What is the number of girls playing only badminton?
(a) 16
(b) 14
(c) 17
(d) Data inadequate
(e) None of these
Ans.b

Let the number of boys= x

then x + 7x10 = 85 or x = 50

No. of girls = 85 – 50 = 35

34

5. When the price of a product was increased by 15%, the number sold was decreased by 20%. What was the net effect?
(a) 8% gain
(b) 5% loss
(c) 8% loss
(d) Cannot be determined
(e) None of these
Ans.c

Net effect = + 15 – 20 – \(\frac{15 \times 20}{100} = -8\%\)

–ve sign indicates loss.

6. If 18 of 23 of 45 of a number is 12 then 30 per cent of the number will be
(a) 48
(b) 64
(c) 54
(d) 42
(e) None of these
Ans.c

Let the number be x.

and 18 of 23 of 45 × x = 12

3x10 = 54

7. Venkat purchased twenty dozens of toys at the rate of 375 per dozen. He sold each one of them at the rate of 33. What was his percentage profit?
(a) 6.5
(b) 5.6
(c) 3.5
(d) 4.5
(e) None of these
Ans.b

Cost price of 20 dozen toys = 20 × 375 = 7,500

Selling price of 20 dozen toys = 20 × 33 × 12 = 7,920

Profit percentage = \(\frac{7920 - 7500}{7500} \times 100 = 5.6\%\)

8. A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?
(a) 35
(b) 30
(c) 25
(d) 20
(e) None of these
Ans.a

Let the truth spoken by A and B be pl and p2

respectively, i.e., pl = 34 and p2 = 45

They will contradict each other only when one speaks truth and the other is lying.

i.e., 34 × 15 + 45 × 14 = 320 + 420 = 720 = 35100 i.e, 35%

9. Pradip spends 40 per cent of his monthly income on food items, and 50 per cent of the remaining on clothes and conveyance. He saves one-third of the remaining amount after spending on food, clothes and conveyance. If he saves 19,200 every year,what is his monthly income?
(a) 24,000
(b) 12,000
(c) 16,000
(d) 20,000
(e) None of these
Ans.c

Food items = 40%

Clothes + conveyance = 12 of 60% = 30%

13 of 30% = 19,20012 ⇒ 10% = 1600

∴ 100% = ₹ 16,000

10. When 30 per cent of a number is added to another number the second number increases by its 20 per cent. What is the ratio between the first and the second number?
(a) 3 : 2
(b) 2 : 3
(c) 2 : 5
(d) Data inadequate
(e) None of these
Ans.b

30% of I + II = II × 120100

or, 310I = 210II ⇒ I : II = 2 : 3.