The age of the farmer 15 years ago was 9 times the age of his wife If the sum of their present ages ...........

Quantitative Aptitude (CDS) Problems based on Ages

The age of the farmer 15 years ago was 9 times the age of his wife. If the sum of their present ages is 80 years. What is the present age of his wife?

16 years

13 years

24 years

20 years

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Explanation:

Let the present age of farmer and wife be x and y years respectively.
From 1st condition,
(x – 15) = 9 (y – 15)
= x – 15= 9y – 135
= x – 9y = – 120 …(i)
From 2nd condition,
= x + y = 80 …(ii)
From equation (i) and (ii)
– 10y = – 200
y = 20
Present age of wife = 20 years