Question

At present, the ratio between the age of Sharmila and Sanju is 5:7 respectively. Sharmila is 12 years younger than Sanju. What is the total of Sharmila and Sanju, 4 years ago?

Answer 1

Hint: Let us assume the present age of Sharmila and Sanju by x years and y years respectively. We have given the ratio of their present ages as 5:7 so equate the ratio of x and y to 5:7. We know that we can write fraction in place of ratio so replace the ratio to fraction. This will be equation (1). After that, we have given Sharmila is 12 years younger than Sanju so we can write this statement in terms of x and y variables as x-y=12. Now, we have two linear equations and two unknowns x and y which we are going to solve by substitution method

Complete step-by-step answer:
In the question, first we will have to find the present ages of Sharmila and Sanju. Let the age of Sharmila be x and the age of Sanju be y. Now, it is given that the ratio between their ages is $\dfrac{5}{7}$, we get the following equation:
$\dfrac{x}{y}=\dfrac{5}{7}$
$\Rightarrow 7x=5y..........(i)$
Now, another condition given in question is that Sharmila is 12 years younger than Sanju. Thus, after applying this condition, we will get the following relation:
$x=y-12......(ii)$
Now, we have to substitute the values of one variable to another variable. So, now we are going to substitute the value of x from equation (ii) into equation (i). After substituting this, we get the following result:
$\begin{align}
  & \Rightarrow 7\left( y-12 \right)=5y \\
 & \Rightarrow 7y-84=5y \\
 & \Rightarrow 7y-5y=84 \\
 & 2y=84 \\
 & \Rightarrow y=42 \\
\end{align}$
Now, we will put this value of y=42 in equation (ii). After doing, we will get:
$\begin{align}
  & \Rightarrow x=42-12 \\
 & \Rightarrow x=30 \\
\end{align}$
Now, we have to determine their ages 4 years ago. Age of Sharmila 4 years ago
$\begin{align}
  & =x-4 \\
 & =30-4 \\
 & =26 \\
\end{align}$
Age of Sanju 4 years ago
$\begin{align}
  & =y-4 \\
 & =42-4 \\
 & =38 \\
\end{align}$
Now the sum of ages of Sharmila and Sanju
=26+38
=64

Note: The above linear equation in two variables can also be solved with the help of elimination method. In this method, we multiply one equation with a particular number and then we will add it in another equation to eliminate one variable.