Correct Answer - Option 2 : 21 years
Given:
The average age of Shikha and Yashika = 24 years
After 10 years the ratio of Yashika and Shikha's age = 8 ∶ 9
Concept used:
Average = (Total sum)/(Total number)
Calculations:
The total sum of Shikha and Yashika's present age = 24 × 2 = 48
Let Yashika and Shikha's age after 10 years be 8x and 9x respectively
So, the present age of Yashika = 8x – 10
The present age of Shikha = 9x – 10
The total sum of present age = 8x – 10 + 9x – 10
⇒ 17x – 20 = 48
⇒ 17x = 68
⇒ x = 4
The present age of Shikha = 9x – 10
⇒ 9(4) – 10 = 26 years
Before 5 years the age of Shikha = 26 – 5 = 21 years
∴ Before 5 years the age of Shikha is 21 years