12 years ago, the sum of the ages of P, Q, and R together was 61 years. The ratio of the present age of P to Q is 2:3, and P is 8 years older than R. If the ratio of the present age of P to S is 5:7, then find the present age of S.

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IBPS PO Prelims Memory Based Paper (Held On: 19 October 2024 Shift 2)

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Answer 1

Define variables:

Let present ages be:

P = 2k

Q = 3k

R = P - 8 = 2k - 8

S = s (unknown)

Use the sum of ages 12 years ago:

12 years ago, sum of ages = 61 years

⇒ (P - 12) + (Q - 12) + (R - 12) = 61

⇒ (2k - 12) + (3k - 12) + (2k - 8 - 12) = 61

⇒ 2k - 12 + 3k - 12 + 2k - 20 = 61

⇒ (2k + 3k + 2k) - (12 + 12 + 20) = 61

⇒ 7k - 44 = 61

⇒ 7k = 105

⇒ k = 15

Calculate P's present age:

P = 2k = 2 × 15 = 30 years

Use ratio of P to S:

P : S = 5 : 7

⇒ 30 : s = 5 : 7

⇒ s = (30 × 7) / 5 = 42 years

Thus, S’s present age is 42 years.