What are the two numbers whose sum is 27 and product is 182?

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14 and 13

15 and 13

11 and 13

20 and 13

answer is A.

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Detailed Solution

Given that the sum of two numbers is 27 and their product is 182.
Let the first number = x.
The second number = 27 – x.
According to the question, their product is 182 i.e.,

x (27 − x) = 182 ⇒ 27 x − x 2 = 182 ⇒ x 2 − 27 x + 182 = 0 ⇒ x 2 − 14 x − 13 x + 182 = 0

Take common factors from each two terms.

⇒ x (x − 14) − 13 (x − 14) = 0

Factorize the equation to get two linear factors.

x (x − 14) − 13 (x − 14) = 0 ⇒ (x − 14) (x − 13) = 0

Equate each factor to zero to find the value of x.

⇒

x – 14 = 0 or x – 13 = 0

⇒

x = 14 or x = 13
Hence, the second number = 27 – x is,
27 – 14 = 13 or 27 – 13 = 14
So, the two numbers are 14 and 13.
Therefore, the correct option is 1.

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