What is the woman age? If

A woman says, “If you reverse my own age, the figures represent my husband’s age . He is, of course, senior to me and the difference between our ages is one- eley- enth of their sum” . The woman’ age is

  1. 23 yrs
  2. 34 yrs
  3. 43 yrs
  4. 45 yrs
Monis Rasool Professor Asked on 20th June 2015 in Maths.
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  • 1 Answer(s)

    Answer: (4) 45 years
    Explanation:-
    Let x and y be the ten’s and unit’s digits.
    Then, woman’s age = (10X + y) years and husband’s age = (10Y + X) years.
    Therefore, (10Y + X) – (10X + Y) = (1/11)(10Y + X + 10X + Y)
    10Y + X – 10X – Y = (1/11)(11X + 11Y)
    9Y – 9X = (1/11)(11Y + 11X)
    9Y – 9X= X + Y
    8Y = 10X
    X = 4Y/5
    Y should be a single-digit multiple of 5
    So, X = 4 and Y = 5
    Hence, the woman’s age = 10 x 4 + 5 = 40 + 5 = 45 years.

    Anurag Mishra Professor Answered on 20th June 2015.
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