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How much percentage more than the cost price should a shopkeeper mark his goods, so that after allowing a discount of 12.5%, he should have a gain of 5% on cost price,
  • a)
    5    
  • b)
    20
  • c)
    25    
  • d)
    40
Correct answer is option 'B'. Can you explain this answer?
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How much percentage more than the cost price should a shopkeeper mark ...
To find the percentage more than the cost price that the shopkeeper should mark his goods, we need to follow a step-by-step approach.

Let's assume the cost price of the goods is 'C'.

Step 1: Calculate the selling price after a discount of 12.5%
The selling price after the discount can be calculated using the formula:
Selling price = Cost price - (Discount percentage * Cost price)
Substituting the values, we get:
Selling price = C - (12.5/100) * C
Selling price = C - 0.125C
Selling price = 0.875C

Step 2: Calculate the gain on the cost price
The gain percentage can be calculated using the formula:
Gain percentage = (Gain/Cost price) * 100
Given that the gain percentage is 5% and the cost price is 'C', we can write:
5 = (Gain/C) * 100
Gain = (5/100) * C
Gain = 0.05C

Step 3: Calculate the marked price
The marked price can be calculated using the formula:
Marked price = Cost price + Gain
Substituting the values, we get:
Marked price = C + 0.05C
Marked price = 1.05C

Step 4: Calculate the percentage more than the cost price
The percentage more than the cost price can be calculated using the formula:
Percentage more than cost price = ((Marked price - Cost price)/Cost price) * 100
Substituting the values, we get:
Percentage more than cost price = ((1.05C - C)/C) * 100
Percentage more than cost price = (0.05C/C) * 100
Percentage more than cost price = 5%

Therefore, the shopkeeper should mark his goods at a price that is 5% more than the cost price in order to have a gain of 5% on the cost price after allowing a discount of 12.5%.

Hence, the correct answer is option 'B' - 5%.
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