Question
Download Solution PDFA lady said, “If you reverse my age digits, you'll get my husband's age. He is older, and the difference between their ages is one-eleventh of their sum." What is the man's age ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Let the lady's age be 10x + y (where x and y are the digits of her age).
The husband's age is 10y + x (reversed digits).
He is older, so 10y + x > 10x + y.
The difference between their ages is one-eleventh of their sum.
Formula used:
(Husband's age) - (Lady's age) = 1/11 × (Husband's age + Lady's age)
Calculation:
⇒ (10y + x) - (10x + y) = 1/11 × [(10y + x) + (10x + y)]
⇒ 9y - 9x = 1/11 × (11y + 11x)
⇒ 9(y - x) = y + x
⇒ 8y = 10x
⇒ y = 5, x = 4
⇒ Lady's age = 10(4) + 5 = 45 years
⇒ Husband's age = 10(5) + 4 = 54 years
∴ The man's age is 54 years.
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