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1. The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :

A. 11 : 9

B. 11 : 18

C. 21 : 19

D. 22 : 19

Solution:

Let the numbers be x and y
Then,

\begin{aligned} \Leftrightarrow \frac{x + y}{x - y} = \frac{40}{4} \\ \Leftrightarrow \frac{x + y}{x - y} = 10 \\ \Leftrightarrow (x + y) = 10 (x - y) \\ \Leftrightarrow 9 x = 11 y \\ \Leftrightarrow \frac{x}{y} = \frac{11}{9} \\ \Leftrightarrow x : y = 11 : 9 \end{aligned}

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