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Question
A woman says, "If you reverse the digits my age, the figures represent my husband's age. He is senior to me and the defference between our ages is one-eleventh of their sum. "What is her age now?
23 years
34 years
45 years
50 years
None of these
ANSWER : 3
Descrption
<p>Let, the unit's digit of woman's age be 'y' and ten's digit be 'x'</p> <p>If so, the woman's age is = (10x + y) years and her husband’s age is = (10y + x) years. [Digits are reversed]</p> <p>ATQ,</p> <p>(10y + x) - (10x + y) = (10y + x) + (10x + y) (1/11)</p> <p>‌‌or, 9y - 9x = (11y + 11x)/11</p> <p>or, 9y - 9x = 11(y + x)/11</p> <p>or, 9y - y = x + 9x</p> <p>or, 10x = 8y</p> <p>or, x = (4/5)y</p> <p>Clearly, y should be a single digit and multiple of 5, which is 5 [only possible value]</p> <p>Hence, y = 5 and x = 4</p> <p>So, woman's age = (10x + y) = 45 years.</p> <p> </p>
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