A merchant purchases a cloth at a rate of Rs. 100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
- 9.7%
- 16%
- 4.2%
- 15.5%
The Correct Option is D
Solution and Explanation
Given that a merchant purchases a cloth at a rate of Rs.\(100\) per meter and receives \(5\) cm length of cloth free for every \(100\) cm length of cloth purchased by him.
So, the cost price of \(105\) cm clothes is \(100\) rupees.
Subsequently, the merchant sets the selling price of \(100\) cm of cloth at \(110 \)rupees but applies a \(5\%\) discount and he cheated his customers by giving \(95\) cm length of cloth for every \(100\) cm length of cloth purchased by the customers.
Therefore, the selling price of \(95\) cm clothes \(=110\times\frac {19}{20}\)
And, the selling price of \(105\) cm clothes \(=115.5\) rupees.
Hence, the profit \(=15.5\%\)
So, the correct option is (D): \(15.5\%\)
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