Hema is 20 years old and her sister Neha is 30 years old. How many years ago were their ages in the ratio of 3 : 5?

Question

Accepted Answer

Let the number of years ago be x.

At that time, Hema's age = 20 - x
Neha's age = 30 - x

According to the problem, their ages were in the ratio 3 : 5.

So, (20 - x) / (30 - x) = 3 / 5

Cross-multiplying:
5(20 - x) = 3(30 - x)
100 - 5x = 90 - 3x

Bring variables to one side:
100 - 90 = 5x - 3x
10 = 2x

x = 5

Wait, this contradicts the initial answer. Let's re-check calculations.

Recalculate:
5(20 - x) = 3(30 - x)
100 - 5x = 90 - 3x

Bring variables to one side:
100 - 90 = 5x - 3x
10 = 2x
x = 5

So, x = 5 years ago.

Check the ages 5 years ago:
Hema: 20 - 5 = 15
Neha: 30 - 5 = 25
Ratio = 15 : 25 = 3 : 5

Therefore, the correct answer is 5 years ago.

Hence, option 4 is correct.

Answer

Answer

Answer