The ratio of two number is 3:2, If 10 and the sum of the

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The ratio of two number is 3:2, If 10 and the sum of the two numbers are added to their product, square of sixteen is obtained. What could be the smaller number ?

1. 14
2. 12
3. 16
4. 18

Correct Option: B

Let the two numbers be 3N and 2N

According to the question.
10 + (3N +2N ) + (3N x 2N) = 16²
⇒ 6N² + 5N - 246 = 0
⇒ 6N² + 41N - 36N - 246 = 0
⇒ N(6N + 41 ) - 6(6N + 41) = 0
⇒ (6N + 41 ) (N - 6) = 0

∴ N = 6 or -41/6 (But -ve value cannot be accepted )
∴ Smaller number = 2N = 2 x 6 = 12 .