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1. The sum of two numbers is 37 and the difference of their squares is 185, then the difference between the two numbers is :

A. 10

B. 4

C. 5

D. 3

Solution:

Let the numbers be a and b, where a > b
According to the question,

\begin{aligned} a + b = 37 & a^{2} - b^{2} = 185 \\ \Rightarrow (a + b) (a - b) = 185 \\ \Rightarrow 37 (a - b) = 185 \\ \Rightarrow a - b = \frac{185}{37} \\ \Rightarrow a - b = 5 \end{aligned}

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