Question

5. My grandfather was 9 times older than me
16 years ago. He will be 3 times of my age 8
years from now. Eight years ago, the ratio of
grandfather to that of the child was

Answer 1

Given:

• Before 16 yrs , my grandfather was 9 times older than me.

Condition:

• He will be 3 times of my age 8 yrs from now.

To Find:

• The ratio of the age of grandfather to me.

Solution:

Before 16 years ago, let my age be x year

then , my grandfather's age will be 9 years

After 8 years from now ,

$\sf9x + 16 + 8 = 3(x + 8 + 16) \\ \sf \implies9x + 16 + 8 = 3x + 24 + 48 \\ \sf\implies \sf9x - 3x =24 + 48 - 16 - 8 \\ \sf \implies6x = 48 \\ \sf \implies \: x = \cancel \frac{48}{6} \\ \implies \sf \: \: x = 8$

Ratio of ages , 8 years ago :

= (x +8):(9x+8)

=(8+8) : (9 × 8+8)

= (16 :80) =( 1:5)

$( \sf \cancel16 \ratio \: \cancel 80) = (1 \ratio \: 5) \\ \implies (1 \ratio5) = (1 \ratio \: 5)$

$\therefore \boxed{ \bold \red {ratio \: of \: their \: age = 1 :5 }}$