**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.

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?

Tags algebra father's age mathematics son's age

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