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If the two digits of the age of Mr. Manoj are reversed then the new age so obtained is the age of his wife. 1/11 of the sum of their ages is equal to the difference between their ages. If Mr. Manoj is elder than his wife then find the difference their ages ?
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- Cannot be determined
- 10 years
- 8 years
- 9 years
Correct Option: C
Let the age of Mr Manoj be (10y + y) yrs.
∴ His wife's age = (10y + x ) years
Then, ((10x + y + 10y + x) / 11 = 10x + y -10y-x
⇒ x + y = 9x - 9y
⇒ 8x = 10y
⇒ x/y = 5/4
∴ x = 5 and y =4 (because any other multiple of 5 will make x of two digits).
∴ Diff. = (10x + y) - (10y - x)
= 9x - 9y
= 9(x-y)
= 9(5-4)
= 9 yrs.
