Find the values of two numbers whose sum is 27 and product is 182?

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12,13

13,14

14,15

15,16

answer is B.

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Detailed Solution

According to the problem, we need to find the numbers whose sum is 27 and product is 182.
Let us assume the two required numbers are ‘a’ and ‘b’.
From the problem, we are given that the sum of these two numbers is 27.
So, we have a+b=27.
⇒b=27−a ---(1).
From the problem, we are given that the product of these numbers is 182.
So, we have ab=182 ---(2).
Let us substitute equation (2) in equation (1).
So, we have a(27−a)=182.
⇒27a−a2=182.
⇒a2−27a+182=0.
⇒a2−13a−14a+182=0.
⇒a(a−13)−14(a−13)=0.
⇒(a−14)(a−13)=0.
⇒a−14=0 or a−13=0.
⇒a=14 or a=13 ---(3).
Let us assume a=14 and substitute this in equation (1).
So, we have b=27−14=13.
∴ The two numbers are 14 and 13.
Let us assume a=13 and substitute this in equation (1).
So, we have b=27−13=14.
∴ The two numbers are 13 and 14.

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