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1. For a certain article. If discount is 25% the profit is 25%. If the discount is 10%, then the profit is = ?

A. 50%

B. 40%

C. 30%

D. $33 \frac{1}{3} %$

Solution:

\begin{aligned} For same article, \\ \frac{100 - d_{1}}{100 - d_{2}} = \frac{100 + g_{1}}{100 + g_{2}} \\ \Rightarrow \frac{100 - 25}{100 - 10} = \frac{100 + 25}{100 + g_{2}} \\ \Rightarrow \frac{75}{90} = \frac{125}{100 + g_{2}} \\ \Rightarrow 100 + g_{2} = \frac{90 \times 125}{75} \\ \Rightarrow 100 + g_{2} = 150 \\ ∴ g_{2} = 50 % \end{aligned}

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