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Question -

FatherтАЩs age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father. (C.B.S.E. 2003)



Answer -

Let fatherтАЩs present age = x years
and sum of ages of his two children = y
then x = 3y
=> y = (1/3) x тАж.(i)
After 5 years,
Age of father = x + 5
and sum of age of two children = y + 2 x 5 = y + 10
(x + 5) = 2(y + 10)
x + 5 = 2y + 20
=> x = 2y + 20 тАУ 5
x = 2y + 15 тАж.(ii)
From (i)
x = 2 x (1/3) x + 15
=> x = (2/3) x + 15
=> x тАУ (1/3) x = 15
=> (1/3) x = 15
=> x = 15 x 3 =45
Age of father = 45 years

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