Question

AA 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-eleventh of their sum. The age of the woman is: (a) 23 years (c) 45 years (b) 34 years (d) 56 years (e) none of these​

Answer 1

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Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age = (10X + y) years; husband's age = (10y + x) years.

Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)

⇔ (9y-9x) = (1/11)(11y + 11x) = (x + y) ⇔ 10x = 8y ⇔ x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.

So, x = 4, y = 5.

Hence, woman's age = 10x + y = 45 years.

Answer 2

Answer:

Here is your answer

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age =(10x+y) years; husband's age =(10y+x) years.

Therefore (10y+x)−(10x+y)=(1/11)(10y+x+10x+y)

⇔(9y−9x)=(1/11)(11y+11x)=(x+y)⇔10x=8y⇔x=(4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.

So, x=4, y=5.

Hence, woman's age =10x+y=45 years.

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