Question

The sum of present ages of Sarthak and Sakshi is 25. Sarthak's age is less by 8 than double the age of Sakshi. What is the present age of Sarthak and Sakshi?

Answer 1

Hint: We are given two statements that contain information regarding the ages of Sarthak and Sakshi. We will use these two statements to form two equations. Both of these equations will have two unknowns, which are the ages of Sarthak and Sakshi respectively. We will solve these two equations simultaneously to obtain the present ages of Sarthak and Sakshi.

Complete step-by-step answer:
Let the present age of Sarthak be $x$ years and let the present age of Sakshi be $y$ years. We are given that the sum of their present ages is 25. So, we can write this in the following manner,
$x+y=25....(i)$
Next, we are given that Sarthak's age is less by 8 than double the age of Sakshi. Double the age of Sakshi is represented by $2y$. So, the given statement can be written as an equation in the following manner,
$x=2y-8....(ii)$
Now we have two linear equations with two unknowns. We will solve these two equations simultaneously. We will use the method of substitution. We will substitute the value of $x$ from equation $(ii)$ in equation $(i)$. We get the following equation,
$2y-8+y=25$
Simplifying the above equation, we get
$\begin{align}
  & 3y-8=25 \\
 & \Rightarrow 3y=25+8 \\
 & \Rightarrow 3y=33 \\
 & \therefore y=11 \\
\end{align}$
Now, substituting this value of $y$ in equation $(ii)$, we get
$\begin{align}
  & x=2\times 11-8 \\
 & \Rightarrow x=22-8 \\
 & \therefore x=14 \\
\end{align}$
Therefore, the present age of Sarthak is 14 years and the present age of Sakshi is 11 years.

Note: The key aspect in this type of questions is to interpret the word problem correctly. After we interpret the problem statements, we should be able to form correct equations. Otherwise, there is a possibility of obtaining an incorrect answer. There are other methods of solving linear equations like Gauss elimination method or graphing.