Question

Sum of brother and sisters age is 26. Four times the brothers age is subtracted from three times the sisters age, the difference is 8. What are the ages of the brother and sister?

Answer 1

Answer : The ages of the brother and sister are, 10 and 16 years respectively.

Solution :

Let the age of brother be 'x' and the age of sister be 'y'

There are two equations formed which are,

x + y = 26      ..........(1)

3y - 4x = 8     ..........(2)

First we have to multiple equation (1) by 4 and then added equation (1) and (2), we get the value of 'y'.

$4x+4y+3y-4x=8+26\\\\7y=112\\\\y=16$

Now put the value of 'y' in equation (2), we get the value of 'x'

3(16) - 4x = 8

4x = 40

x = 10

The age of brother = x = 10 years

The age of sister = y = 16 years

Therefore, the ages of the brother and sister are, 10 and 16 years respectively.