Question

Raman's present age is three times his daughter's present age and nine-thirteenth of his mother's present age. The sum of their present ages is 125. What is the difference between Raman's daughter's present age and Raman's mother's present age?

• A. 45 years
• B. 40 years
• C. 50 years
• D. Cannot be determined
• E. None of these

Answer 1

The correct option is C 50 years

Here, Raman's present age = x years

It is given that Raman's present age $=3\times$ daughter's present age

$\therefore$ His daughter's present age $=\frac{x}{3}$ years

And, it is also given that Raman's present age $=\frac{9}{13}\times$ mother's present age

His mother's present age $=\frac{13x}{9}$ years

And, Sum of their ages $=125$

$\therefore x+\frac{x}{3}+\frac{13x}{9}=125$

$\Rightarrow \frac{9x+3x+13x}{9}=125$

$\Rightarrow \frac{25x}{9}=125$

$\Rightarrow x=125\times \frac{9}{25}$

$\Rightarrow x=45$ years

So, Raman's present age $=x=45$ years

$\therefore$ His daughter's present age $=\frac{x}{3}=\frac{45}{3}=15$ years

His mother's present age $=\frac{13x}{9}=\frac{13\times 45}{9}=65$ years

So, the difference between Raman's daughter's present age and Raman's mother's present age $=65-15=50$ years