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Question

Two years ago Sam's age was 412 times the age of his son. Six years ago, his age was twice the square of the age of his son. What is the present age of Sam's son ?

A
20
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B
10
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C
15
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D
13
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Solution

The correct option is D 10
Let m be the age of Sam and s be the age of his son
Then, 2 years ago,
(m2)=92(s2)
2m4=9s18
2m=9s14...(i)
6 years ago,
(m6)=2(s6)2
(9s1426)=2(s6)2
9s1412=4(s212s+36)
9s26=4s248s+144
4s257s+170=0
s=57±5298 = 57±238=10,4.25
Neglect the 4.25 which is a fraction.
Hence, age of his son is 10 years.

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