Question

Five year ago, Gowri was 5 times as old as Ganesh, 5 years later Gowri’s age will be 20 years more than Ganesh. How old are Gowri and Ganesh?

Answer 1

Hint: At first suppose the present ages of Ganesh And Gowri be x, y respectively. Then according to the given condition for ages 5 years ago form an equation and formulate another from the given condition of present age. Then solve it simultaneously to get an answer.

Complete step-by-step answer:
In the question, we are given two situations where the age of Gowri and Ganesh is compared which is five years ago, Gowri was 5 times as old as Ganesh and five years later Gowri’s age will be twenty years more than Ganesh.
Now, let Ganesh’s and Gowri’s present ages be x, y respectively. So, let’s take the first case of five years ago.
 So, five years ago the ages of Ganesh and Gowri were $\left( x-5 \right),\left( y-5 \right)$ respectively.
At that time, the age of Gowri was five times as old as Ganesh. So, we can write according to the question as,
$\left( y-5 \right)=5\left( x-5 \right)$
So, on simplification we get
$y-5=5x-25$
Now adding 5 to both sides, we get
$y=5x-20$ …....................................(i)
So, now let’s the 2nd case in five years later.
So, five years later the age of Ganesh and Gowri will be $\left( x+5 \right)$ and $\left( y+5 \right)$. We can write according to the question,
$y+5=\left( x+5 \right)+20$
On simplification, we get
$y+5=x+25$
Now subtracting 5 from both sides, we get
$y=x+20$ ………………………….(ii)
Now from both the cases, we get two versions of y in terms of ‘x’. So, now we will equate it.
$5x-20=x+20$
Now, taking all the variable terms on one side and constant on the other side. So, we get
$4x=40$
Hence, the value of x is 10.
Now, for finding y we will substitute the value of x in equation(i). We will get
$y=5\times 10-20=30$
Hence, the value of y is 30.
The present age of Gowri and Ganesh is 30 and 10 respectively.

Note: This question can also be done by using a single variable. Let’s assume the present age of Ganesh is x so, it’s 5 years ago age will be $\left( x-5 \right)$ then Gowri's age 5 years ago will be $5\left( x-5 \right)$ or $5x-25$ . So, Gowri’s present age will be $5x-25+5$ or $5x-20$ . Now proceed further with given values of ages in terms of t.