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Four friends born between (1991 – 99) meets at 2020. The ratio of sum of age of two oldest guys: Sum of age two youngest guys is 9 ∶ 8. Again when they meet at 2030, the ratio of (sum age of youngest + oldest) and (sum of ages of other two) is 1 ∶ 1. What is the sum of the age of the third youngest guy and second youngest guy in the year 2020? (in years)

Four friends born between (1991 – 99) meets at 2020. The ratio of sum of age of two oldest guys: Sum of age two youngest guys is 9 ∶ 8. Again when they meet at 2030, the ratio of (sum age of youngest + oldest) and (sum of ages of other two) is 1 ∶ 1. What is the sum of the age of the third youngest guy and second youngest guy in the year 2020? (in years) Correct Answer 51

If all the 4 people were born between 1991 – 99, their ages at 2020 should be in the range 21 – 29

By year 2020

Let the age of the guys (from youngest to oldest) in the year 2020 be p, q, r and s respectively

Let sum of ages of two oldest guys and sum of ages two youngest guys be 9a and 8a respectively

9a and 8a should lie between 42 – 58 (Because sum of two people)

Only such value is possible when a = 6

Sum of ages of two youngest = p + q = 48      ---- 1

Sum of ages of two oldest = r + s = 54      ---- 2

By the year 2030

Their ages will be p + 10, q + 10, r + 10 and s + 10

Sum of ages of oldest + youngest: Sum of ages of other two guys = 1 ∶ 1

⇒ p + s + 20 = q + r + 20

∴ p + s = q + r

Equation 1 + Equation 2

⇒ p + s + q + r = 102

⇒ 2 × (q + r) = 102

⇒ q + r = 51 years

∴ The sum of the age of the third youngest guy and second youngest guy in the year 2020 is 51 years.

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