The sum of the ages of father and his son is 45 years. Five years ago, the product of their ages was 34. The age of father is:
Answer & explanation
Correct answer: option 3
The best way to find answer:
Check answer options and satisfy two equations:
a) F + S = 45 and b) (F - 5)(S - 5) = 34
Now,
F : S (F-5) × (S-5)
a) 40 : 5 ⇒ 35 × 1 ≠ 34
b) 15 : 30 ⇒ Not possible
c) 39 : 6 ⇒ 34 × 1 = 34
d) 38 : 7 ⇒ 33 × 3 ≠ 34
Hence, Father's age is = 39 years
Alternate way:
Father's age = F
Son's age = S
Five years ago father's age = F -5
Five years ago son's age = S -5
ATQ,
F + S = 45 years
(F - 5) × (S - 5) = 34
FS - 5F -5S + 25 = 34
FS -5 (F + S) = 9
FS - 5(45) = 9
FS = 234
F (45 - F) = 234 .......(i)
Put and check answer options:
From option (3)
put F = 39 years in equation (i)
39 (45 - 39) = 234
234 = 234
Hence, Father's age = 39 years.