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Question 4

If 40% of a number is added to another number then it becomes 125% of itself. The ratio of the second to the first number is

Solution

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Let the first number be $$x$$ and the second be $$y$$. Adding 40% of the first to the second gives 125% of the second: $$y + 0.4x = 1.25y$$, so $$0.4x = 0.25y$$, giving $$\frac{y}{x} = \frac{0.4}{0.25} = \frac{8}{5}$$. So the ratio of the second to the first number is $$8 \colon 5$$.

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