Currently Hema is 48 years old and Roja is 32 years old. How many years ago was the ratio of their ages 5 : 3?

Correct option is C

Given:

Hema's current age = 48 years

Roja's current age = 32 years

Required ratio of ages = 5:3

Solution: 

From the given condition;

$$\frac{\text{Hema’s age }48 - x)}{\text{Roja's age } (32 - x)} = \frac{5}{3}$$ 

​$$\frac{48 - x}{32 - x} = \frac{5}{3} ​$$​​

​$$(48 - x) \times 3 = (32 - x) \times 5$$​​

144 - 160 = -5x + 3x

−16 = −2x

x = 8 

Thus , 8 years ago there age was in the ratio 5 : 3.