# If a sum of Rs. 53 is divided among P, Q and R in such a way that P gets Rs. 7 more than Q and Q gets Rs. 8 more than R gets, the ratio of their share

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If a sum of Rs. 53 is divided among P, Q and R in such a way that P gets Rs. 7 more than Q and Q gets Rs. 8 more than R gets, the ratio of their shares is
1. None of these
2. 16 : 17 : 19
3. 25 : 18 : 10
4. 21 : 10 : 22

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Correct Answer - Option 3 : 25 : 18 : 10

Given:

P gets 7 more than Q

Q gets 8 more than R gets

Total sum = Rs. 53

Calculation:

Let the share of R be Rs. x

Q gets 8 more than R gets, Q = x + 8

P gets 7 more than Q gets, P = (x + 8) + 7 = x + 15

Total sum = (P + Q + R)'s sum = x + 8 + x + 15 + x = 3x + 23

According to the question

⇒ 3x + 23 = 53

⇒ 3x = 30

⇒ x = 10

Ratio of P, Q and R share is

⇒ (x + 15) : (x + 8) : x

⇒ (10 + 15) : (10 + 8) : 10

⇒ 25 : 18 : 10

∴ The ratio of their shares is 25 : 18 : 10