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1. A trader allows a trade discount of 20% and a cash discount of $6 \frac{1}{4} %$ on the marked price of the goods and gets a net gain of 20% of the cost. By how much above the cost should the goods be marked for the sale = ?

A. 40%

B. 50%

C. 60%

D. 70%

Solution:

\begin{aligned} Single equivalent discount \\ = (20 + \frac{25}{4} - \frac{20 \times 25}{400}) % \\ = 25 % \end{aligned}

Let cost price of article = Rs. 100
∴ Selling price of article = Rs. 120 (20% profit)
Let the marked price of article = Rs. x

\begin{aligned} ∴ x \times \frac{75}{100} = 120 \\ \Rightarrow x = \frac{120 \times 100}{75} \\ \Rightarrow x = Rs . 160 \\ Required percentage \\ = \frac{160 - 100}{100} \times 100 \\ = 60 % \end{aligned}

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