Question

The sum of ages of a mother and daughter is $45$ years. Five years ago, the product of their ages was four times the mother's age at that time. The present age of the mother is?

• A. $38$ years
• B. $37$ years
• C. $36$ years
• D. $39$ years

Answer 1

The correct option is C $36$ years

Let the present age of the mother be $x$ years.

It is given that the sum of ages of a mother and daughter is $45$. Therefore, the presentage of the daughter is $(45-x)$ years.

Five years ago, the mother's age was $(x-5)$ and the daughter's age was $(45-x)-5=(40-x)$

Now, it is also given that five years ago, the product of their ages was four times the mother's age at that time, therefore, we have:

$(x-5)\times (40-x)=4(x-5)\Rightarrow (x-5)\times (40-x)=4(x-5)\Rightarrow (40-x)=\frac{4(x-5)}{(x-5)}\Rightarrow 40-x=4\Rightarrow x=40-4\Rightarrow x=36$

Therefore, the mother’s age is $36$ years and her daughter's age is:

$45-x=45-36=9$ years.

Hence, the present age of the mother is $36$ years.