QUESTION

# Two ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Hint: Here we assume the ages of persons given in the problem as variables and then according to the given condition we try to establish a relationship between those variables as equations. After solving these equations we can easily find out the solution.

Complete step-by-step solution -
Age of Biju – Age of Ani = 3 years.
Age of Dharam = 2(Age of Ani).
Age of Biju = 2(Age of Cathy)
And, age of Dharam – Age of Cathy = 30

Let the age of Ani be ‘A’, of Biju be ‘B’, of Cathy be ‘C’ and that of Dharam be ‘D’.
Then, according to question,
We have, B – A = 3 ………. (i)
D = 2A ………. (ii)
B = 2C ………. (iii)
And D – C = 30 ………. (iv)
Now, we have to find the value of A and B
Since, (D – C) = 30 [from (iv)]
$\Rightarrow$2A – C = 30 [from (iv)&(ii)]
$\Rightarrow 2A - \dfrac{B}{2} = 30$ [ $\because B = 2C$ from (iv)]
$\Rightarrow 2A - \left( {\dfrac{{A + 3}}{2}} \right) = 30$ [$\because$ $B - A = 3 \Rightarrow B = A + 3$]
$\Rightarrow \dfrac{{4A - A - 3}}{2} = 30 \\ \Rightarrow 3A - 3 = 60 \\ \Rightarrow 3A = 63 \\$
$\Rightarrow A = \dfrac{{63}}{3} = 21$ ……. (v)
$\Rightarrow B = 21 + 3 = 24$ [From (i) and (v)]
Hence, the age of Ani is 21 years and that of Biju is 24 years.

Note: To solve this type of questions we need to read the questions carefully. Then make equations accordingly. Once our equations are ready, we can use them to get the desired result.