Question

Sudhir's present age is 5 more than three times the age of Viru. Anil's age is half the age of Sudhir. If the ratio of the sum of Sudhir's and Viru's age to three times Anil's age is 5:6, then find Viru's age.

Answer 1

Let Viru's present age be x years.
Sudhir's present age = (5 + 3x) years
Anil's present age = $\left(\frac{5+3x}{2}\right)$ years

∴ From the given information,
$$\begin{gathered} \left(5+3x\right)+\left(x\right):3\frac{\left(5+3x\right)}{2}=5:6 \\ \Rightarrow \frac{5+4x}{{\displaystyle \frac{3\left(5+3x\right)}{2}}}=\frac{5}{6} \\ \Rightarrow \frac{2\left(5+4x\right)}{15+9x}=\frac{5}{6} \\ \Rightarrow \frac{10+8x}{15+9x}=\frac{5}{6} \\ \Rightarrow 6\left(10+8x\right)=5\left(15+9x\right) \\ \Rightarrow 60+48x=75+45x \\ \Rightarrow 48x-45x=75-60 \\ \Rightarrow 3x=15 \\ \Rightarrow x=5 \end{gathered}$$

Hence, Viru's age is 5 years.