Question

Ten years ago a father was seven times as old as his son, two years hence. Twice his age will
be equal to five times his son’s. What is present age of son?
a) 20 years
b) 14 years
c) 22 years
d) 13 years

Answer 1

Option(b) 14 years is the answer.

Let f = father's present age
Let s = son's present age

Ten years ago a father was seven times as old as his son,
(f-10) = 7(s-10)
f - 10 = 7s - 70
f = 7s - 70 + 10
f = 7s - 60

two years hence twice his age will be equal to five times his son's age.
2(f + 2) = 5(s + 2)
2f + 4 = 5s + 10
2f = 5s + 10 - 4
2f = 5s + 6

Substitute (7s-60) for f in the above equation:
2(7s - 60) = 5s + 6
14s - 120 = 5s + 6
14s - 5s = 6 + 120
9s = 126
s=126÷9
●s = 14 yr's is son's present age

 f = 7s - 60
f = 7(14) - 60
f = 98 - 60
●f = 38 yrs is father's present age


HOPE IT HELPS YOU.
Mark my answer as brainliest.

Answer 2

Answer:

age of son is 14years

age of father is 38 years