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The sum of the present ages of a father and his son is 18 years more than 4 times the present age of the son. After 5 years, 4 times the father's
Question

The sum of the present ages of a father and his son is 18 years more than 4 times the present age of the son. After 5 years, 4 times the father's age will be 8 years less than 14 times the son's age. The difference (in years) between the present ages of the father and the son is:

A.

49

B.

45

C.

48

D.

53

Correct option is C

Given:
The sum of the present ages of a father and his son is 18 years more than 4 times the present age of the son.
After 5 years, 4 times the father's age will be 8 years less than 14 times the son's age.
Solution:
The sum of their present ages:
f + s = 4s + 18 
f + s = 4s + 18
f = 4s + 18 - s = 3s + 18 (Equation 1)
The condition after 5 years:
4(f + 5) = 14(s + 5) - 8 (Equation 2)
Substitute Equation 1 into Equation 2:
4((3s + 18) + 5) = 14(s + 5) - 8
4(3s + 23) = 14s + 70 - 8
12s + 92 = 14s + 62
92 - 62 = 14s - 12s
30 = 2s
s = 15
f = 3(15) + 18 = 45 + 18 = 63
f - s = 63 - 15 = 48

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