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
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