Question

Ten years ago,a man's age was thrice as old as his son .in ten years time,the man's age will be twice as old as his son.Find their present ages

Answer 1

M = man's present age

S = son's present age

Ten years ago man was M - 10 yrs old, and son was S - 10 yrs old.

man's age was thrice as old as his son means:

M - 10 = 3 ( S - 10 )

M - 10 = 3 S - 30

Add 10 to both sides

M = 3 S - 20

After 10 years man will be M+ 10 yrs old, and son will be S + 10 yrs old.

in ten years time,the man's age will be twice as old as his son means:

M + 10 = 2 ( S + 10 )

M + 10 = 2 S + 20

Subtract 10 to both sides

M = 2 S + 10

M in first formula for man's age is equal to M in second formula for man's age.

M = M

3 S - 20 = 2 S + 10

Subtract 2 S to both sides

S - 20 = 10

Add 20 to both sides

S = 30

Son is 30 yrs old

First formula for man's age gives:

M = 3 S - 20

M = 3 • 30 - 20 = 90 - 20 = 70

Second formula for man's age also gives:

M = 2 S + 10

M = 2 • 30 + 10 = 60 + 10 = 70

Man is 70 yrs old

Check result.

Ten years ago man was 60 yrs old, and son was 20 yrs old.

60 / 20 = 3

After 10 years man will be 80 yrs old, and son will be 40 yrs old.

80 / 40 = 2