Profit and Loss with Dishonest Merchant

CAT 2023 Slot 3 · QA · Medium · Arithmetic

All CAT 2023 Slot 3 questionsMore Arithmetic questionsAll CAT QA

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

  1. A.

    4.2%

  2. B.

    15.5%

  3. C.

    16%

  4. D.

    9.7%

Answer

B

Explanation

Cost Price per cm: For Rs. 100, the merchant gets 100+5=105100 + 5 = 105 cm. CP per cm=100105=2021 Rs/cm\text{CP per cm} = \frac{100}{105} = \frac{20}{21}\text{ Rs/cm}

Selling Price per cm: Marked Price = Rs. 110 per meter. With 5%5\% discount, SP per meter charged to customer = 110×0.95=104.5110 \times 0.95 = 104.5 Rs. For 100 cm paid by customer, merchant actually gives 95 cm. SP per cm=104.595=1.1 Rs/cm\text{SP per cm} = \frac{104.5}{95} = 1.1\text{ Rs/cm}

Profit Percentage: Profit %=(SPCP−1)×100=(1.120/21−1)×100=(23.120−1)×100=15.5%\text{Profit \%} = \left(\frac{\text{SP}}{\text{CP}} - 1\right) \times 100 = \left(\frac{1.1}{20/21} - 1\right) \times 100 = \left(\frac{23.1}{20} - 1\right) \times 100 = 15.5\%

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace