Understanding money and age via ratio and proportion

Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

Hyderabad: This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.
1. A certain sum of money was divided among P, Q and R in a certain way. Q received one-third of what P and R together did and P got one-fourth of what Q and R together did. Find the ratio of shares of P, Q and R respectively.
a) 4 : 5 : 10 b) 5 : 4 : 10 c) 4 : 5 : 11 d) 5 : 4 : 11
Ans: c
Solution: According to the question:
Q = 1/3 × (P R)

⇒ 3Q = P R………. (i)
P = 1/4 × (Q R)
⇒ 4P = Q R………….. (ii)

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P = (Q R) /4
Putting the value of P in equation (i)
3Q = (Q R) /4 R
⇒ 12Q = Q R 4R
⇒ 12Q = Q 5R

⇒ 11Q = 5R
Q/R = 5/11

Let Q = 5x and R = 11x

Putting the values of Q and R in equation (i)
3 × 5x = P 11x
⇒ 15x = p 11x

⇒ P = 4
P : Q : R = 4x : 5x : 11x = 4 : 5 : 11
2. A man divides Rs 1,25,000 among his 4 wives: 2 times the share of the first wife, 3 times the share of the second wife, 4 times the share of third wife and 6 times the share of the fourth wife are equal. Find the amount received by the third wife?
a) Rs 50000 b) Rs 40000 c) Rs 35000 d) Rs 25000
Ans: d
Solution: Let W1, W2, W3 and W4 be his 4 wives.
Given that,
W1 W2 W3 W4 = 125000 …(i)
2W1 = 3W2 = 4W3 = 6W4 = k
Substituting the value in terms of k in (i)
k (1/2 1/3 1/4 1/6) = 125000
k (15/12) = 125000
k = 100000
Amount received by third wife
= k/4 = 100000/4 = 25000
3. The present age of Arjun and Radhika is in the ratio 3 : 2 respectively. 9 years ago, the ratio of age of Arjun and Shyam was 4 : 5 respectively and Radhika was 10 years younger than Shyam. What will the ratio of age of Arjun and Shyam after 3 years?

a) 2 : 3 b) 4 : 5 c) 5 : 6 d) 8 : 9

Ans: d

Solution: Let the present age of Arjun and Radhika be 3x and 2x respectively

So, y – 2x = 10 y = 10 2x …(i)

(3x – 9)/5 = 4/(y – 9)

15x – 45 = 4y – 36
15x – 45 = 4 (10 2x) – 36

15x – 45 = 40 8x – 36

x = 7

y = 24

Reqd. ratio = 3x 3 / y 3 = 21 3/ 24 3 = 8 : 9

To be continued…

M. Venkat

Director
MVK Publications
Dilsukhnagar
7671002120