The average age of a man and his son is 40 years the ratio of their age is 7:3 respectively what is the man's age
m = man's age
s = son's age
The average age of a man and his son is 40 years means:
( m + s ) / 2 = 40
Multiply both sides by 2
m + s = 80
the ratio of their age is 7:3 means:
m / s = 7 / 3
Multiply both sides by s
m = 7 / 3 s
Put this value in equation:
m + s = 80
7 / 3 s + s = 80
7 / 3 s + 3 / 3 s = 80
10 / 3 s = 80
Multiply both sides by 3
10 s = 240
s = 240 / 10 = 24 yrs
m = 7 ∙ 24 / 3 = 168 / 3 = 56 yrs