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Kapil is the elder brother of Kunal and their ages are in double digits. The difference between their ages is one-eleventh of the sum of their ages. If the digits of the age of Kapil are reversed, we get Kunal’s age. What is the age of Kunal?

Kapil is the elder brother of Kunal and their ages are in double digits. The difference between their ages is one-eleventh of the sum of their ages. If the digits of the age of Kapil are reversed, we get Kunal’s age. What is the age of Kunal? Correct Answer 45

Let the age of Kapil be 10x + y.

If the digits of the age of Kapil are reversed, we get Kunal’s age.

So, the age of Kunal is 10y + x.

The difference between their ages is one-eleventh of the sum of their ages.

Difference between their age = (10 x + y) – (10y + x)

= 10x + y – 10y – x

= 9x – 9y

= 9 (x – y)

Sum of their ages = (10x + y + 10y + x)

= (11x + 11y)

= 11 (x + y)

According to question:

9 (x – y) = (1/11) × 11 (x + y)

⇒ 9 (x – y) = (x + y)

⇒ 9x – 9y = x + y

⇒ 9x – x = y + 9y

⇒ 8x = 10y

⇒ x/y = 10/8

⇒ x/y = 5/4

Therefore, x = 5 and y = 4

So, the age of Kunal = 10y + x = 10 × 4 + 5 = 40 + 5 = 45

Hence, ‘45’ is the correct answer. 

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