Question

A shopkeeper marks his books at 25% above the cost price. Due to slump in the market, his cost reduces by 5%. And then, to boost his sale, he offered a discount of 8% due to which sales goes up by 25%. Compute the change in the shopkeepers profit.

• A. No change
• B. 7% change
• C. 2.5% change
• D. 8% change

Answer 1

The Correct Option is A

To determine the change in the shopkeeper's profit, we can calculate the profit margins before and after the cost reduction and discount offer. Let's solve this step-by-step: 

1. \(Let \, C \, be \, the \, original \, cost \, price.\) Therefore, the marked price is: \(M = C + 0.25C = 1.25C\)
2. Initial selling price (SP) with a discount of 8%: \(SP_{initial} = M(1 - 0.08) = 1.25C \times 0.92 = 1.15C\)
3. Initial profit percentage: \(Profit \%_{initial} = \left( \frac{SP_{initial} - C}{C} \right) \times 100 = \left( \frac{1.15C - C}{C} \right) \times 100 = 15\%\)
4. New cost price due to 5% reduction in cost: \(C_{new} = C(1 - 0.05) = 0.95C\)
5. New marked price at 25% above the new cost price: \(M_{new} = 0.95C \times 1.25 = 1.1875C\)
6. New selling price with 8% discount on the new marked price: \(SP_{new} = 1.1875C \times 0.92 = 1.092C\)
7. New profit percentage: \(Profit \%_{new} = \left( \frac{SP_{new} - C_{new}}{C_{new}} \right) \times 100 = \left( \frac{1.092C - 0.95C}{0.95C} \right) \times 100 = 15\%\)

From the calculations, we can see that the initial profit percentage was 15%, and the new profit percentage is also 15%. Therefore, there is no change in the shopkeeper's profit despite the adjustment in cost and sales strategy.