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Integers

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Question

What is the sum of two number whose difference is 45, and the quotient of the greater number when divided by the lesser number is 4?

A

100

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B

90

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C

80

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D

75

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Solution

The correct option is B $75$
Let the lesser number be $x$ Then
Greater number $= x + 45$
Given $\frac{x + 45}{x} = 4 \Rightarrow x + 45 = 4 x$
$\Rightarrow 3 x = 45 \Rightarrow x = 15$
Then required sum $= x + x + 45 = 30 + 45 = 75$

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