Question

A has three daughters whose ages are in the ratio 7 ∶ 8 ∶ 9 (at present). Their husbands are 3, 2 and 6 years respectively elder to their wives. Each one of the couple has a child whose age is 1/5^th the sum of ages of their parents. If sum of age of the grandchildren of A is 31, then what is the sum of ages of the son-in-laws of A? (in years) All the ages are measured at present.
1. 80
2. 81
3. 82
4. 83
5. 84

Answer 1

Correct Answer - Option 4 : 83

Let the ages of the daughters be 7a, 8a and 9a respectively

∴ Ages of their husbands = 7a + 3, 8a + 2 and 9a + 6

Age of the kid of first couple = 1/5 × (7a + 7a + 3)

⇒ 1/5 × (14a + 3) = 2.8a + 0.6

Age of the kid of second couple = 1/5 × (8a + 8a + 2)

⇒ 3.2a + 0.4

Age of the kid of third couple = 1/5 × (9a + 9a + 6)

⇒ 3.6a + 1.2

Sum of ages of grandkids of A = 2.8a + 0.6 + 3.2a + 0.4 + 3.6a + 1.2

⇒ 9.6a + 2.2 = 31

⇒ 9.6a = 29.8

∴ a = 3

Ages of husbands = 21 + 3 = 24

⇒ 24 + 2 = 26

⇒ 27 + 6 = 33

∴ Sum of ages of son-in-laws = 24 + 26 + 33 = 83 years