Question

5 years ago, the mother's age was 3 times of her son's age. 5 years hence, the ratio between the ages of mother and the son becomes 11:5. Find the mother's present age?

Answer 1

50 years

Explanation:

Let 5 years ago the age of son be x years

Given that

mother's age was 3 times of her son's age

5 years ago the age of mother was 3x years

Then present age of son will be 5 years more than age he had 5 years ago

present age of son = (x+5) years

similarly present age of mother = 3x+5 years

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Let calculate age 5 year hence

5 year hence age of son = present age of son + 5 years

5 year hence age of son = (x+5) years + 5 years = x + 10 years

5 year hence age of mother = present age of mother + 5 years

5 year hence age of mother = (3x+5) years + 5 years = 3x + 10 years

Given that

ratio between the ages of mother and the son becomes 11:5

thus,

3x+10/x+10 = 11/5

=> 5(3x+10) = 11(x+10)

=> 15x+50 = 11x+110

=> 15x-11x = 110-50

=> 4x= 60

=> x = 60/4 = 15

Thus, value of x is 15 years

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We have present age of mother as 3x+5, substituting valye of x as 15

3x+5 = 3*15+5 = 45+5 = 50

Mother's present age is 50 years.