Question

The ages of Hari and Harry are in the ratio of $5:7$. Four years from now the ratio of their ages will be $3:4$. Find their present ages.

Answer 1

Step 1: Assuming the age of Hari and Harry in terms of variable

Let the age of Hari be $5x$.

Let the age of Harry be $7x$.

Four years hence,

The age of Hari$=$ $5x+4$

The age of Harry $=7x+4$

Step 2: Finding the value of $x$

According to the question,

The ratio of their ages will be

$$\begin{gathered} \Rightarrow \frac{5x+4}{7x+4}=\frac{3}{4} \\ \Rightarrow 4(5x+4)=3(7x+4) \\ \Rightarrow 20x+16=21x+12 \\ \Rightarrow 16-12=21x-20x \\ \Rightarrow 4=x \end{gathered}$$

Step 3: Finding the age of Hari and Harry

Hence,

The present age of Hari $=5x=5\times 4=20yrs$

The present age of Harry $=7x=7\times 4=28yrs$