Akram is older than his wife. If the digits of his wife’s are reversed, it will represent the Akram's age. The difference between their ages is 1/11 of their sum, the woman’s age is?
- 22 years
- 45 years
- 34 years
- None of these
Explanation
Let's denote Akram's age as 10a + b and his wife's age as 10b + a, where a > b.
Given the difference between their ages is 1/11 of their sum:
(10a + b) - (10b + a) = 1/11 * ((10a + b) + (10b + a))
9a - 9b = 1/11 * (11a + 11b)
9(a - b) = a + b
9a - 9b = a + b
8a = 10b
4a = 5b
Possible values for (a, b) given a > b:
(5, 4)
Akram's age: 10_5 + 4 = 54
Wife's age: 10_4 + 5 = 45
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