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Home / Algebra / 20 years ago, father’s was 5 times as old as his son. After 5 years three times of father’s age will be equal to five times of son’s age. What are the present age’s of father and son?

20 years ago, father’s was 5 times as old as his son. After 5 years three times of father’s age will be equal to five times of son’s age. What are the present age’s of father and son?

Solution: Let, the present age of the father be x and that of the son be y years.
∴ 20 years ago father was = x-20 years
and 20 years ago son was = y-20 years.
Again, 5 years later father will be = x+5 years
∴ 5 years later son will be = y+5 years
According to the first condition
x-20=5(y-20) ———————– (1)
and according to the second condition
3(x+5)=5(y+5) ———————(2)
In the first equation we get,
x-20=5y-100
⇒ x=5y-100+20
⇒x=5y-80 ————————-(3)
Putting the value of x from third equation in second equation we get,
3(5y-80+5)=5(y+5)
⇒ 3(5y-75)=5y+25
⇒ 15y-225=5y+25
⇒15y-5y=25+225
⇒10y=250
⇒y=25
∴ y=25
Putting the value of y in the third equation we get,
x=5.25-80
= 125-80
=45
∴ Father’s age 45 years and son’s age 25 years.

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