Question

Father's age is three times the sum of Ages of his two children. after 5 years his age will twice the sum of Ages of two children. find the age of father?

Answer 1

Let the sons age be x and y.
so According to question (A.T.Q)
Father's age = 3×(x+y)
= 3x + 3y -- eq 3
Also,
after five years the ages of two children be (x+5) and (y+5)
So, Father's age after 5 years = 2×(x+5+y+5)
= 2(x+y+10)
Now In second case father's age increases by 5 years as it is after 5 years from the first case so to make it equal to the age to the first case we will subtract 5 from both sides in second case ,that is
Father's age after 5 years - 5 = 2(x+y+10)-5
= 2x + 2y +20 -5
= 2x + 2y + 15 -- eq 2
Now LHS becomes equal in both cases.
Now subtracting eq 2 from 1

3x + 3y + 0 = Father's age
- 2x + 2y + 15 = Father's age after 5 years
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x + y - 15 = 0 ( 0 because Father's age and Father's age after 5 years is equal, so their subtraction equals 0)
x + y = 15 ( by transportation method)

Now we were given that Father's age is three times sum of ages of sons
So
Father's age = 3 × 15 = 45 years

Answer 2

Let the sum of son’s age be m. Then father’s age us 3m
After 5 years sum of son’s age= m + 2*5 = m+10

Father’s age after 5 years will be 3m+5

But it is given that 3m+5 = 2(m+10)
m= 15

So father’s age= 3*15 = 45 years