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There are 5 members in Prajakta's family. Prajakta's husband is 5 years older than her and they have 2 sons and Prajakta's father in law is twice the age of her husband. The ratio between the present age of the elder son and the age of the younger son 1 year later is 2 ∶ 1 and the ratio between the present age of younger son and his father is 1 ∶ 5. What is the average age of the family if the ratio between the age of Prajakta two years later and his husband one year later is 8 ∶ 9?

There are 5 members in Prajakta's family. Prajakta's husband is 5 years older than her and they have 2 sons and Prajakta's father in law is twice the age of her husband. The ratio between the present age of the elder son and the age of the younger son 1 year later is 2 ∶ 1 and the ratio between the present age of younger son and his father is 1 ∶ 5. What is the average age of the family if the ratio between the age of Prajakta two years later and his husband one year later is 8 ∶ 9? Correct Answer 31.6 years

Let the present age of Prajakta be x

Then, the present age of her husband = x + 5

Now, According to question

The ratio between the age of Prajakta two year later and his husband one year later is 8 ∶ 9

⇒ (x + 2)/(x + 6) = 8/9

⇒ 9x + 18 = 8x + 48

⇒ x = 30

∴ Present age of Prajakta = 30 yrs

Present age of Prajakta's husband = 35 yrs

The ratio between the present age of younger son and his father is 1 ∶ 5

Let the age of the younger son and his father be x and 5x respectively

⇒ 5x = 35

⇒ x = 7

∴ Present age of younger son = 7 yrs

Now, the ratio between the present age of the elder son and the age of the younger son 1 year later is 2 ∶ 1

⇒ S/8 = 2/1

⇒ S = 16 

S → Present age of elder son

∴ Present age of elder son = 16 yrs

Age of Prajakta's father in law = 2 × 35 = 70 yrs

∴ Average age of the family = (30 + 35 + 7 + 16 + 70)/5 = 31.6 yrs

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