Question

Mrs. Joseph is 27 years older than her daughter Bindu. After 8 years she will be twice as old as Bindu. Find their present age.

Answer 1

Hint: We first assume the present ages of Bindu and then find her mother’s age. We have the relation that after 8 years she will be twice as old as Bindu. We express it in mathematical terms and solve the linear equation to get their ages.

Complete step by step answer:
Let the present age of Bindu be x years. Mrs. Joseph is 27 years older than her daughter Bindu.
So, the present age of Mrs. Joseph is $\left( x+27 \right)$ years.
It’s given that after 8 years she will be twice as old as Bindu.
After 8 years the age of Mrs. Joseph will be $\left( x+27 \right)+8=x+35$ years and the age of Bindu will be $\left( x+8 \right)$ years.
So, $\left( x+35 \right)$ is twice of $\left( x+8 \right)$. We express it in mathematical terms and get $\Rightarrow \left( x+35 \right)=2\left( x+8 \right)$.
We solve the equation and get the value of x.
 $\begin{align}
  & \Rightarrow x+35=2x+16 \\
 & \Rightarrow x=19 \\
\end{align}$

So, the present age of Bindu is 19 years and the present age of Mrs. Joseph is $\left( 19+27 \right)=46$ years.

Note: Instead of taking one variable we could also have taken Mrs. Joseph’s age as one more variable y. Then we have got one more equation involving their difference in age as 27. Two equations for two variables. We solve the rest in similar ways.