Rajan's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 years. What is the difference between the present ages of Rajan's daughter and Rajan's mother ?
Answer: C
Let Rajan's present age be '\(x \)' years.
Then his daughter's present age is = \(\frac{x}{3}\) years.
His mother's present age = \(\frac{13x}{9}\) years.
Now, according to the question,
\(\therefore x+\frac{x}{3}+\frac{13x}{9}=125\)
\(\Rightarrow x=\)\(\frac{125*9}{25}\)\(=45\)
Therefore, required difference = \(\frac{13x}{9}-\)\(\frac{x}{3}=13x -\)\(\frac{3x}{9}=\)\(\frac{10x}{9}\)
\(\Rightarrow \frac{10*45}{9}\)= 50 years