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Profit on selling 10 candles equals selling price of 3 bulbs. While loss on selling 10 bulbs equal selling price of 4 candles. Also profit percentage equals to the loss percentage and cost of a candle is half of the cost of a bulb. What is the ratio of selling price of candles to the selling price of a bulb?

A. 5 : 4 B. 3 : 2 C. 4 : 5 D. 3 : 4 Answer: Option B
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Solution(By Apex Team)

While buying, Let the cost price of the candles be x then the cost price of bulbs is 2x Let the selling price of candles be a and that of bulbs be b then $\begin{array}{|c|c|c|} \hline & \text { Candles } & \text { Bulbs } \\ \hline \text { Cost Price } & \text { x } & \text { 2x } \\ \hline \text { Selling Price } & \text { a } & \text { b } \\ \hline \end{array}$ Condition 1: Profit percentage = $\frac{3 \mathrm{~b}}{10 \mathrm{x}} \times 100$ Condition 2: Loss percentage $=\frac{4 a}{20 x} \times 100$ Profit percentage = Loss percentage $\begin{array}{l}\Rightarrow\frac{3\mathrm{~b}}{10\mathrm{x}}\times100=\frac{4\mathrm{a}}{20\mathrm{x}}\times100\\ \Rightarrow3\mathrm{~b}=2\mathrm{a}\\ \Rightarrow\frac{3}{2}=\frac{\mathrm{a}}{\mathrm{b}}\\ \therefore\mathrm{a}:\mathrm{b}=3:2\end{array}$

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