Age#2.Mother’s age is three times more than her son Amit’s age. After 8 years, she would be two and a half times of Amit’s age. After further 8 years, how many times would she be of Amit’s age?

a. 2 times

b. 3 times

c. 4 times

d. None of the above.

Solution: In our previous question [Age#1] we solved the problem by using concept of linear equation in two variables. So in this question we will make use of another method i.e using only one variable to solve the problem. We will apply the same technique to solve the problem i.e spliting up the given part of the question and forming equations of each part.

Given: “Mother’s age is three times more than her son Amit’s age.” Let Amit’s age be x. Therefore mother’s age is (3 times more than x) i.e equal to, (3x+x) = 4x. First part is over.

Now, 2^{nd} part, “After 8 years, she would be two and a half times of Amit’s age.” We can write it as,

4x + 8 = (2 and ½) times x+8

Or, 4x + 8 = 5/2 times x+8

Or, 4x + 8 = 5 (x+8) / 2

Or, 2(4x + 8) = 5x +40

Or, 8x + 16 = 5x + 40

Or, 8x-5x = 40-16

Or, 3x = 24

Or, x = 24/3

Or, x= 8. So, present age of Amit is 8 yrs and mother’s present age is 4 x 8 = 32 yrs.

After 8 yrs Amit would be (8+8) =16 yrs old and his mother would be 40 yrs old, which is two and half times more than Amit’s age. (verified)

And after 8 more years Amit would be 16+8 = 24yrs old and Mother’s age would be 40+8 = 48 yrs. But we need to find “how many times would she be of Amit’s age, now after 8 more years”. We just need to find the ratio of mother’s age to Amit’s age.i.e. 48/24 =2 times. Mother would be 2 times more than Amit’s age after 8 more years. Correct option is (a) 2 times. Correct option is (a) 2 times.