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Question -

Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son. (C.B.S.E. 2004)



Answer -

Let present age of father = x years
and age of his son = y years
2 years ago,
age of father = x – 2
and age of son = y – 2
x – 2 = 5(y – 2)
=> x – 2 = 5y – 10
=> x = 5y – 10 + 2
=> x = 5y – 8 ………(i)
2 years later,
age of father = x + 2
and age of son = y + 2
x + 2 = 3 (y + 2) + 8
=> x + 2 = 3y + 6 + 8
=> x = 3y + 14 – 2 = 3y + 12 ….(ii)
From,(i) and (ii)
5y – 8 = 3y + 12
=> 5y – 3y = 12 + 8
=> 2y = 20
=> y = 10
From (i)
x = 5y – 8 = 5 x 10 – 8 = 50 – 8 = 42
Present age of father = 42 years
and age of son = 10 years

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