A shopkeeper marks a product 75% above cost price and offers two successive discounts of 30% and 40%. What is the profit or loss percentage?
26.5% loss
To determine the profit or loss percentage when the shopkeeper applies two successive discounts on a marked-up product, we will follow these steps:
- Let's denote the cost price (CP) of the product as \(C\).
- The marked price (MP) is 75% above the cost price. Therefore, the marked price is: \(MP = C + 0.75C = 1.75C\)
- The shopkeeper applies a first discount of 30% on the marked price. The new selling price (SP1) becomes: \(SP1 = MP \times (1 - 0.30) = 1.75C \times 0.70 = 1.225C\)
- A second discount of 40% is applied to \(SP1\), giving the final selling price (SP2): \(SP2 = SP1 \times (1 - 0.40) = 1.225C \times 0.60 = 0.735C\)
- The profit or loss is determined by comparing the final selling price (SP2) to the cost price (C). Since \(SP2\) is lower than \(C\), there is a loss. The loss amount is: \(\text{Loss} = C - SP2 = C - 0.735C = 0.265C\)
- The percentage loss is calculated as: \(\text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 = \left(\frac{0.265C}{C}\right) \times 100 = 26.5\%\)
Therefore, the result is a 26.5% loss.
Hence, the correct answer is: 26.5% loss.
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