Question

A family consists of five people, Tina's brother is 6 years elder to her and the ratio of age of Tina 1 year ago and Tina's grandfather's present age is 1 ∶ 4, the ratio of the present age of her mother and father is 15 ∶ 16, the ratio of her father's and grand father's age is  2 ∶ 3.Tina's mother is 20 years elder to Tina's brother. Find the average age of the family (approximate value)?
1. 38 years
2. 48 years
3. 42 years
4. 45 years

Answer 1

Correct Answer - Option 3 : 42 years

 The ratio of age of Tina 1 year ago and Tina's grandfather's present age is 1 ∶ 4

⇒ Let the present age of Tina and Tina's grandfather be x + 1, 4x

The ratio of her father's and grand father's age is  2 ∶ 3

∴ Tina's father age = 2/3(4x) = 8x/3

Tina's brother's age = x + 1 + 6 = x + 7

The ratio of the present age of her mother and father is 15 ∶ 16

⇒ Present age of Tina's Mother = (15/16) × (8x/3) = 5x/2

Now, Tina's mother is 20 years elder to Tina's brother

⇒ (5x/2) – (x + 7) = 20

⇒ x = 18

Tina's age = 18 + 1 = 19

Tina's brother age = 18 + 7 = 25

Tina's fathers age = (8 × 18)/3 = 48

Tina's mothers age = (5 × 18)/2 = 45

Tina's grandfather age = 4 × 18 = 72

∴ Avearge age of the family = (19 + 25 + 48 + 45 + 72)/2 = 41.8 or 42 years

∴ Avearge age of the family is 42 years