Question

Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one third of the mother's present age. What are their present ages?

• A. Present age of Shobo is $7$ years and his mother is $42$ years
• B. Present age of Shobo is $18$ years and his mother is $54$ years
• C. Present age of Shobo is $5$ years and his mother is $30$ years
• D. Present age of Shobo is $8$ years and his mother is $48$ years

Answer 1

The correct option is C Present age of Shobo is $5$ years and his mother is $30$ years

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

Then, Shobo's mother's age $=6x$ years

After $5$ years: Shobo's age $=(x+5)$ years

$\therefore (x+5)=\frac{1}{3}\times \left(6x\right)$

On cross multiplying, we get

$3\times (x+5)=6x$

$\Rightarrow 3x+15=6x$

$\Rightarrow 3x-6x=-15$

$\Rightarrow -3x=-15$

$\Rightarrow x=5$

Therefore, present age of Shobo is $5$ years and his mother is $30$ years.