To determine how many years ago Sindhu was three times as old as Smita, we can set up the equation based on their current ages. Currently, Sindhu is 40 years old and Smita is 20 years old.
Let’s denote the number of years ago we need to find as x. At that time, Sindhu’s age would have been (40 – x) and Smita’s age would have been (20 – x).
According to the problem, we want to find the number of years ago when Sindhu was three times as old as Smita:
40 - x = 3 * (20 - x)
Now, let’s solve the equation:
- First, distribute the 3 on the right side:
40 - x = 60 - 3x
- Next, add 3x to both sides and subtract 40 from both sides:
2x = 20
- Now, divide both sides by 2:
x = 10
This means that 10 years ago, Sindhu was three times as old as Smita. To verify:
- Ten years ago, Sindhu was 30 years old (40 – 10) and Smita was 10 years old (20 – 10).
- Indeed, 30 is three times 10, so our calculation is correct.
In conclusion, Sindhu was three times as old as Smita 10 years ago.