Question

The present age of Rohit and Mayank are in the ratio of 4 : 3. After 9 years, the ratio of their ages will be 11: 9. Find their present ages.

Answer 1

Hint: In the question given to us, we will assume the present ages of Rohit and Mayank to be 4x and 3x. So, after 9 years, their ages will become, $4x+9$ and $3x+9$. Now we have been given that after 9 years, their ages would be in the ration of 11 : 9, so we will equate the ratio of their ages after 9 years to this ratio. We will then solve the thus obtained equation and get the value of x. We will then substitute the value of x in their present age to get the required answer.

Complete step by step answer:
The question given to us is about the application of ratio in word problems. To understand the question, we must know about the concept of ratio. A ratio indicates the number of times, one number contains the other number. For example, if the mass of boy 1 = 2 kg and if the mass of boy 2 = 3 kg, then the ratios of the mass of boy 1 to boy 2 would be equal to 2 : 3.
Now, in the given question, we have been given the present age ratio of Rohit and Mayank as 4 : 3. We know that ratio is generally expressed in the simplest form and is unitless. Thus, it may be so in this question too, and may not be the exact value. So, we have to consider a value x as a common part. So, let us assume the present ages of Rohit and Mayank to be 4x and 3x. We have been given that after 9 years, the ratio becomes 11: 9. So, their ages will change after 9 years as,
Rohit = $4x+9$
Mayank = $3x+9$
We know the ratio of their ages would be,
$\dfrac{4x+9}{3x+9}$
The value of this ratio is given to us as, $\dfrac{11}{9}$, so we will equate them. So, we get an equation as,
$\dfrac{4x+9}{3x+9}=\dfrac{11}{9}$
On doing cross-multiplication, we get,
$\begin{align}
  & 9\left( 4x+9 \right)=11\left( 3x+9 \right) \\
 & \Rightarrow 36x+81=33x+99 \\
\end{align}$
Taking the x terms to one side and the constants to the other, we get,
$\begin{align}
  & 36x-33x=99-81 \\
 & \Rightarrow 3x=18 \\
 & x=6 \\
\end{align}$
So, we get the value of x as 6. So, we can calculate the present ages of Rohit and Mayank as,
Rohit = $4x=4\times 6=24$ years
Mayank = $3x=3\times 6=18$ years.

Note:
 We can solve this question in an alternate way also. We can start by considering their age after 9 years as 11x and 9x. So, according to the conditions in the question, their age 9 years ago would be, $11x-9$ and $9x-9$ whose ratio would be 4 : 3. So, we can equate them as, $\begin{align}
  & \dfrac{11x-9}{9x-9}=\dfrac{4}{3} \\
 & \Rightarrow 3\left( 11x-9 \right)=4\left( 9x-9 \right) \\
 & \Rightarrow 33x-27=36x-36 \\
 & \Rightarrow 36-27=36x-33x \\
 & \Rightarrow 3x=9 \\
 & \Rightarrow x=3 \\
\end{align}$
So, we get the value of x as 3, so Rohit’s age would be $11x=11\times 3=33$ years, so he would be 33 - 9 = 24 years presently. And similarly, Mayank would be $9x=9\times 3=27$ years, so he would be 27 - 9 = 18 years presently.