# The average age of Shikha and Yashika is 24 years and after 10 years the ratio of Yashika and Shikha's age is 8 ∶ 9 then find before 5 years what is t

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The average age of Shikha and Yashika is 24 years and after 10 years the ratio of Yashika and Shikha's age is 8 ∶ 9 then find before 5 years what is the age of Shikha.
1. 16 years
2. 21 years
3. 26 years
4. 31 years

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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