Q5 of 23 Page 1

Attempt any two sub-questions from the following:

When the son will be as old as his father today, the sum of their ages then will be 126 years. When the father was as old his son is today. The sum of their ages then was 38 years. Find their present ages.

Let the present age of son = x

and the present age of father = y


Difference in their ages = y - x


Given, when the ages will be as old as father today their ages will add up to 126 years


⇒ {x + (y - x)} + {y + (y - x)} = 126


⇒ {x + y - x} + {y + y - x} = 126


⇒ y + 2y - x = 126


⇒ 3y - x = 126 .................(1)


Again, when the father as old as son is today, their ages add up to 38 years


⇒ {y + (x - y)} + {x + (x - y)} = 38


⇒ {y + x - y} + {x + x - y} = 38


⇒ x + 2x - y = 38


⇒ 3x - y = 38 .................(2)


Multiply by 3 in equation (2), we get


⇒ 9x - 3y = 114 ..............3


Add equation 1 and 3, we get


8x = 240


⇒ x = 240/8


⇒ x = 30


From equation (1), we get


3y - 30 = 126


⇒ 3y = 126 + 30


⇒ 3y = 156


⇒ y = 156/3


⇒ y = 52


So, the present age of son = x = 30 years


and the present age of father = y = 52 years


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