Question

a grandfather is 9 times older than his granddaughter. In 8 years the grandfather will be 5 times older than his granddaughter. How old is each of them now?

Answer 1

Given:

A grandfather is 9 times older than his granddaughter.

In 8 years the grandfather will be 5 times older than his granddaughter.

To find:

The present age of grandfather and granddaughter.

Solution:

Let x be the present age of granddaughter.

Then, present age of grandfather = 9x

After 8 years,

Age of granddaughter = x+8

Age of grandfather = 9x+8

In 8 years the grandfather will be 5 times older than his granddaughter.

`9x+8=5(x+8)`

`9x+8=5x+40`

Isolate variable terms.

`9x-5x=-8+40`

`4x=32`

Divide both sides by 4.

`x=8`

Now,

Present age of granddaughter = 8

Present age of grandfather = 9(8) = 72

Therefore, the present age of granddaughter is 8 years and present age of grandfather is 72 years.