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The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :
Answer & Solution
Correct Answer:
Option
A
Let the numbers be x and y
Then,
$$\eqalign{ & \Leftrightarrow \frac{{x + y}}{{x - y}} = \frac{{40}}{4} \cr & \Leftrightarrow \frac{{x + y}}{{x - y}} = 10 \cr & \Leftrightarrow \left( {x + y} \right) = 10\left( {x - y} \right) \cr & \Leftrightarrow 9x = 11y \cr & \Leftrightarrow \frac{x}{y} = \frac{{11}}{9} \cr & \Leftrightarrow x:y = 11:9 \cr} $$
Then,
$$\eqalign{ & \Leftrightarrow \frac{{x + y}}{{x - y}} = \frac{{40}}{4} \cr & \Leftrightarrow \frac{{x + y}}{{x - y}} = 10 \cr & \Leftrightarrow \left( {x + y} \right) = 10\left( {x - y} \right) \cr & \Leftrightarrow 9x = 11y \cr & \Leftrightarrow \frac{x}{y} = \frac{{11}}{9} \cr & \Leftrightarrow x:y = 11:9 \cr} $$
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