Question

The present ages of Mohit and Mayank are in the ratio of $11:8$. After 8 years, their ages will be $5:4$. Find their present ages.

Answer 1

Step 1. Obtain the required equation.

Present ages of Mohit and Mayank are in the ratio of $11:8$.

After 8 years, the ratio of their ages will be $5:4$.

Let the Present age of Mohit be$11x$ and the age of Mayank be $8x$.

After $8$ years, the age of Mohit will be $11x+8$

The age of Mayank will be $8x+8$

After $8$ years, the ratio of their ages will be $5:4$.

So, $\begin{array}{rcl}\frac{11x+8}{8x+8}& =& \frac{5}{4}\end{array}$

Step 2.Solve the obtained equation to determine their present ages.

Solve the equation:

$\begin{array}{ccl}\frac{11x+8}{8x+8}\begin{array}{cl}=& \frac{5}{4}\end{array}& & \\ & & \Rightarrow 4(11x+8)=5(8x+8)\\ \begin{array}{cl}\Rightarrow & 44x+32=40x+40\end{array}& & \\ \begin{array}{cc}\Rightarrow & 44x-40x=40-32\end{array}& & \\ \begin{array}{cl}\Rightarrow & 4x=8\end{array}& & \\ \begin{array}{cl}\Rightarrow & x=\frac{8}{4}\end{array}& & \\ \begin{array}{cl}\Rightarrow & x=2\end{array}& & \end{array}$

Hence, the present ages of Mohit and Mayank are:

$$\begin{gathered} \mathrm{Mohit}\text{'}\mathrm{s}\mathrm{age}=11x \\ =11\times 2 \\ =22 \end{gathered}$$.

and

$$\begin{gathered} \mathrm{Mayank}\text{'}\mathrm{s}\mathrm{age}=8\mathrm{x} \\ =8\times 2 \\ =16 \end{gathered}$$

Hence, the present ages of Mohit and Mayank are $22$ and $16$ respectively.