Question

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)
1. 51
2. 52
3. 53
4. 54
5. 55

Answer 1

Correct Answer - Option 1 : 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.