Question

The sum of the present ages of Manish and Savita is 31. Manish's age 3 years ago was 4 times the age of Savita. Find their present ages.

Answer 1

Hint: In this question, we are given two statements regarding the present ages and ages before 3 years of Manish and Savita. We need to find their present ages. For this, we will first suppose their present ages as x and y. Then we will form two equations from the given statement. Solving these equations will give us the present ages of Manish and Savita.

Complete step by step answer:
Let us suppose that, the present age of Manish is x years and the present age of Savita is y years.
We are given that, the sum of their present ages is 31.
Therefore, we can say that, the sum of x and y us 31. In mathematical form we can say,
 $ x+y=31\cdots \cdots \cdots \left( 1 \right) $ .
Now we are given a statement regarding their ages 3 years ago. So let us find their ages 3 years ago.
Three years ago, the age of Manish will be equal to (x-3) years.
The age of Savita will be equal to (y-3) years.
We are given that Manish's age 3 years ago was 4 times the age of Savita.
So we can say that (x-3) was 4 times (y-3).
In mathematical terms we can say that, $ \left( x-3 \right)=4\left( y-3 \right) $ .
Simplifying the equation we get: $ x-3=4y-12 $ .
Taking variables on one side and the constant on the other side we get: $ x-4y=3-12\Rightarrow x-4y=-9\cdots \cdots \cdots \left( 2 \right) $ .
Now let us solve these two equations (1) and (2) to find the value of x and y.
Subtracting (2) from (1) we get: $ x+y-\left( x-4y \right)=31-\left( -9 \right) $ .
Simplifying we get: $ x+y-x+4y=31+9\Rightarrow 5y=40 $ .
Dividing both sides by 5 we get: $ y=\dfrac{40}{5}\Rightarrow y=8 $ .
Putting values of y in equation (1) we get $ x+8=31\Rightarrow x=31-8=23 $ .
Hence values of x and y are 23 and 8 respectively.
Since x was supposed to be the age of Manish and y was supposed to be the age of Savita.
So, Manish's present age is 23 years.
Savita's present age is 8 years.

Note:
 Students often make mistake while forming equations from statement. They can make mistakes of writing $ 4\left( x-3 \right)=\left( y-3 \right) $ instead of $ \left( x-3 \right)=4\left( y-3 \right) $ . Make sure to write units as years in the final answer. Take care of signs while solving the equation.