Exercise : 4


1. There is a ratio of 5 : 4 between two numbers. If forty percent of the first number is 12 then what would be the 50 percent of the second number?
(a) 12
(b) 24
(c) 18
(d) Data inadequate
(e) None of the above
Ans.a

ab = 54, b = 45a Given (40% of a) = 25a = 12

a = 5 × 6 and b = 45 × 5 × 6 = 24

∴ 50% of b = 242 = 12

2. An amount of money is to be distributed among P, Q and R in the ratio of 5 : 8 : 12 respectively. If the total share of Q and R is four times that of P, what is definitely P’s share?
(a) 3,000
(b) 5,000
(c) 8,000
(d) Data inadequate
(e) None of these
Ans.d

P : Q : R = 5 : 8 : 12

\(\frac{Total \; share \; of \; Q \; and \; R}{Share \; of \; P} = \frac{8 + 12}{5} = \frac{20}{5} = 4\)

So, we see that no new information has been given in the question and P’s share can’t be determined.

3. When 30 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
(a) 3 : 4
(b) 4 : 3
(c) 3 : 2
(d) Data inadequate
(e) None of these
Ans.b

Let the first and the second numbers be x and y respect then

y + 30% of x = 140% of y

or, y + 0.3x = 1.4y

or, 0.3x = 0.4y

∴ x : y = 0.4 : 0.3 = 4 : 3

4. If 25% of a number is subtracted from a second number the second number reduces to its five-sixths. What is the ratio between the first number and the second number?
(a) 2 : 3
(b) 3 : 2
(c) 1 : 3
(d) Data inadequate
(e) None of these
Ans.a

Let the first and second number be x and y respectively.

x - y × 25100 = y × 56

or, y - x4 = 56y

or, 16y = x4y

\ x : y = 2 : 3

5. Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s amount. At the end of the year 20% profit was earned which was equal to 98,000. What was the amount invested by R?
(a) 2,10,000
(b) 1,05,000
(c) 1,75,000
(d) Data inadequate
(e) None of these
Ans.b

Ratio for amount invested by P, Q & R

= 5x × 12 : 6x × 12 : 6x × 6

= 60x : 72x : 36x

= 5x : 6x : 3x

Profit = 98000 = 20% of T

where, T = Total amount

T = 490000

Amount received by

R = \(\frac{3x}{3x + 6x + 5x}\left ( 490000 \right )\)

= 105000

6. One year ago the ratio of Yamini’s and Gamini’s ages was 6 : 7 respectively. Four years hence this ratio would become 7 : 8. How old is Gamini?
(a) 35 years
(b) 30 years
(c) 31 years
(d) Cannot be determined
(e) None of these
Ans.e

Y : G = 6 : 7; One year before

Y : G = 7 : 8; After 4 years

Now, 1 → 5

∴ 7 → 35

Therefore, the age of Gamini now is 35 + 1 = 36 years

7. Ratio of present age of P and Q is 7 : 3. After four years their ages are in the ratio of 2 : 1. What is the present age of P ?
(a) 24 years
(b) 28 years
(c) 32 years
(d) Data inadequate
(e) None of these
Ans.b

PQ = 73 ⇒ Q = 37P.....(i)

also,2Q + 8 = P + 4

or, 2Q – P = – 4...(ii)

Combining equations (i) and (ii), we get

P = 28 years

8. If 40 per cent of a number is added to an other number then it becomes 125 per cent of itself. What will be the ratio of first and second numbers?
(a) 8 : 5
(b) 5 : 7
(c) 5 : 8
(d) Data inadequate
(e) None of these
Ans.e

40x100 + y = 125x100xy = 2017

9. An amount of money is to be divided among P, Q and R in the ratio of 4 : 9 : 16. If R gets 4 times more than P, what is Q’s share in it?
(a) 1,800
(b) 2,700
(c) 3,600
(d) Data inadequate
(e) None of these
Ans.d

Here, neither the total amount nor the individual amount is given. So the share of Q cannot be determined.

10. Jagtap purchases 30 kg of wheat at the rate of 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30 per cent profit?
(a) 16.30
(b) 18.20
(c) 15.60
(d) 14.80
(e) 15.40
Ans.a

CP = 30 × 11.50 + 20 × 14.25 = 630

SP = 630 × 130100 × 150 ≈ 16.30