Question

Sindhu is $40$ years old and Smita is $20$years old. How many years ago were Sindhu three times as old as Smita?

Answer 1

Hint: First, the given that Sindhu is two times greater in age compared to Smita is that Sindhu is $40$ years old and Smita is $20$ years old.
Since we have to find in which year Sindhu is three times older than Smita.
Using the mathematical approach first convert the given problem into mathematical terms and then we can simply solve by using any of the methods like comparison of both statements into one equation

Complete answer:
Let us fix the value of the three years ago that we need to find as X (years).
Given that, Sindhu is $40$years old and three years ago Sindhu was $40 - X$.
Also, from the given that, Smita is $20$years old and three years ago Smita's age is $20 - X$.
According to the question, Sindhu is three times as old as Smita.
So let us compare both values with Sindhu age in $3$ times of Smita age, then we get $40 - X = 3(20 - X)$ (converting the given question in the mathematical equation)
Hence solving this step by step, we get, $40 - X = 3(20 - X) \Rightarrow 40 - X = 60 - 3X$ (by multiplication operation)
$40 - X = 60 - 3X \Rightarrow 3X - X = 60 - 40$(In the left side equation with variables and constant in the right side)
$3X - X = 60 - 40 \Rightarrow 2X = 20$ (By the subtraction operation)
$2X = 20 \Rightarrow X = 10$ (By the division operation)
Hence, we get the value of $X = 10$ which means in $10$ years ago the Sindhu age is three times old as Smita age. Hence the required result.

Note:
We can simply able to solve this problem without converting it into a mathematical equation.
Given that Sindhu is $40$ years old and Smita is $20$ years old, they ask us to find them in what years Sindhu is three times as old as Smita.
If Sindhu needs to be three times old as Smita then the only possibility that Sindhu age is $30$ and Smita age is $10$ (both of the years was decreased to ten)
Hence Smita is three times less than Sindhu's age. Thus, ten years ago is the only possibility.