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:

Question

Accepted Answer

1. **Cost Price Calculation**:
   - The merchant pays Rs.100 for every meter (100 cm) of cloth.
   - For every 100 cm purchased, he receives an additional 5 cm free.
   - Total cloth received = $$ 105 \, 	ext{cm} $$ for Rs.100.
   - Effective cost price per cm = $$ \frac{100}{105} \approx 0.9524 \, 	ext{Rs/cm} $$.

2. **Selling Price Calculation**:
   - The merchant sells the cloth at Rs.110 per meter (or Rs.1.1 per cm).
   - However, he gives only $$ 95 \, 	ext{cm} $$ of cloth for every 100 cm sold.
   - Selling price for $$ 95 \, 	ext{cm} $$ = $$ 95 	imes 1.1 = 104.5 \, 	ext{Rs} $$.
   - After providing a 5% discount, the effective selling price becomes:
     $$
     SP = 104.5 - (0.05 	imes 104.5) = 104.5 	imes 0.95 = 99.275 \, 	ext{Rs}.
     $$

3. **Profit Percentage**:
   - Total money collected by the merchant per transaction:
     $$
     SP_{	ext{effective}} = \frac{99.275}{95} = 1.045 \, 	ext{Rs/cm}.
     $$
   - Cost price per cm is $$ 0.9524 \, 	ext{Rs/cm} $$.
   - Profit percentage:
     $$
     Profit\% = \left( \frac{SP_{	ext{effective}} - CP}{CP} ight) 	imes 100
     $$
     Substituting values:
     $$
     Profit\% = \left( \frac{1.045 - 0.9524}{0.9524} ight) 	imes 100 = 15.5\%.
     $$

Thus, the resulting profit earned by the merchant is **15.5%**, corresponding to option **B**.

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