Question

please solve it step by step ​

Answer 1

ANSWER:-

Given:

A boy is three years younger than his sister. If his age three years ago was two- thirds her age at that time.

To find:

What are their present age.

Solution:

Let R be the boy age &

Let S be the sister age.

According to the question:

S= R +3...........(1)

3 years ago:

R - 3= (2/3)(S-3).........(2)

Substitute equation (1) into (2), we get;

$= > R - 3 = ( \frac{2}{ 3})(R+ 3 - 3) \\ \\ = > R- 3 = \frac{2}{3} \times R \\ \\ = > R- 3 = \frac{2R}{3} \\ \\ = > 3R - 9 = 2R \\ \\ = > 3R - 2R = 9 \\ \\ = > R = 9 \: years$

So,

Putting the value of R in equation (1), we get;

S= 9 +3

S= 12 years.

Verification:

Using equation (2), we get;

$= > 9 - 3 = ( \frac{2}{3} )(12 - 3) \\ \\ = > 6 = \frac{2}{3} \times 9 \\ \\ = > 6 = 2 \times 3 \\ \\ = > 6 = 6 \: \: \: \: [verified]$

Hence,

The present age of boy is 9 years. &

The present age of sister is 12 years.

Hope it helps ☺️