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Question
Father's age is three times the sum of age of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.
Solution
Let the present age of father be x years and the present ages of his two children’s be y and zyears.
The present age of father is three times the sum of the ages of the two children’s. Thus, we have
`x=3(y+2)`
`⇒ y+z=x/5`
After 5 years, father’s age will be (x+5) years and the children’s age will be (y+5) and (z+5) years. Thus using the given information, we have
`x+5 =2 {(y+5)+(z+5)}`
`⇒ x+5 =2 (y+5+z+5)`
`⇒ x = 2(y+z)+20-5`
`⇒ x = 2 (y+z)+15`
So, we have two equations
`y+z =x/3`
`x=2(y+z)+15`
Here x, y and z are unknowns. We have to find the value of x.
Substituting the value of (y+z) from the first equation in the second equation, we have
By using cross-multiplication, we have
`x = (2x)/3+15`
`⇒ x=(2x)/3=15`
`⇒ x(1-2/3)=15`
`⇒ x/3=15`
`⇒ x= 15xx3`
`⇒ x =45`
Hence, the present age of father is 45 years.
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