The sum of the ages of ahsan and his mother is 61 years. The difference in their ages is 29 years. By forming a pair of simultaneous linear equations, find (i) ahsan's present age (ii) the age of ahsan's mother when ahsan is 21 years old

a. 16 years

b. 50 years

Step-by-step explanation:

Let us assume the age of Ahsan be X

And, the age of his mother be Y

It is mentioned in the question that the sum of the both ages to be 61 years and their difference is 29 years

So now the equation is as follows

X + Y = 61 ... (1)

-X + Y = 29 ... (2)

Now solve this

We get

2Y = 90

Y = 45 = Ahsan mother age age

Now put the value of Y in any of the above equation

So X would be

X = 61 - 45

= 16 i. e ahsan age

The mother age is

= 45 years + 5 years

= 50 years

The 5 years come from

= 21 years - 16 years

= 5 years