Question

Ten years ago, Sunil was half of Sudip's age. If the age of both at present is in the ratio of $3:4$, what will be the total of their present age?

• A. $20$ years
• B. $30$ years
• C. $35$ years
• D. $45$ years

Answer 1

The correct option is C $35$ years

Let Sunil's age $10$ years ago be $x$ years.

Since, it is given that Sunil was half of Sudip's age, therefore, Sudip's age $10$ years ago will be $2x$ years.

So, the present age of Sunil is $x+10$ and Sudip's present age is $2x+10$

Also, the present ages of both is in the ratio $3:4$, that is:

$\frac{x+10}{2x+10}=\frac{3}{4}\Rightarrow 4(x+10)=3(2x+10)\Rightarrow 4x+40=6x+30\Rightarrow 4x-6x=30-40\Rightarrow -2x=-10\Rightarrow 2x=10\Rightarrow x=\frac{10}{2}\Rightarrow x=5$

Therefore, the present age of Sunil is $5+10=15$

Sudip's present age is $(2\times 5)+10=10+10=20$

Thus, the total of their present ages is $15+20=35$ years.

Hence, the total of their present ages is $35$ years.