Question

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 mather ?
A) 32 years
B) 48 years
C) 62 years
D) 50 years

Answer 1

Let Rajan's present age be 'x' years.
=> Then his daughter's present age is = x/3 years.
His mother's present age = 13x/9 years
Now, according to the question,
x + x/3 + 13x/9 = 125
=> x = 125x9/25 = 45
Therefore, required difference = 13x/9 - x/3 = 13x - 3x/9 = 10x/9
=> 10 x 45/9 = 50 years.

Answer 2

ANSWER


STEP BY STEP SOLUTION


Let present age of Rajan =x


therefore

Rajen daughter age is

$= \frac{x}{3}$


Rajen mother age is

$= \frac{13x}{9}$

ACCORDING TO QUESTIONS



SUM OF PRESENT AGE OF All


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


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



$= > 25x = 125 \times 9$



$x = \frac{1125}{25}$


$x = 45$


so mean

AGE OF RAJAN=45 years


AGE OF Rajan daughter= 15years


AGE OF Rajan mother


$= \frac{13x}{9}$



$\frac{13 \times 45}{9}$


$= 13 \times 5$


$= 65years$


therefore difference between age of Rajan's daughter and Rajan's mother


=65years-15years


=50years