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प्रश्न
A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find the their present ages.
उत्तर
Let the present age of father be x years and the present age of son be y years.
Father is three times as old as his son. Thus, we have
`x=3y`
`⇒ x-3y=0`
After 12 years, father’s age will be `(x+12)` years and son’s age will be `(y +12)` years. Thus using the given information, we have
`x+12=2(y+12)`
`⇒ x+12=2y+24`
`⇒ x-2y -12=0`
So, we have two equations
`x-3y=0`
`x-2y-12=0`
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
`x/((-3)xx(-12)-(-2)xx0)=(-y)/(1xx(-12)-1xx0)=(1)/(1xx(-2)-1xx(-3))`
`⇒ x/(36-0)=(-y)/(-12-0)=1/1`
`⇒ x/36=(-y)/(-12)=1/1`
`⇒ x/36=y/12=1`
`⇒ x= 36 , y = 12`
Hence, the present age of father is 36 years and the present age of son is 12 years.
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