A businessman lost 20% of his goods due to rain. The remaining items w

A businessman lost 20% of his goods due to rain. The remaining items were sold at a profit of 50%. The businessman earned an overall profit of:

10%

30%

20%

40%

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CISF-AC-EXE – 2023

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Assume the total cost price of the goods was ₹ 100. Let the total quantity be 100 units, so the cost per unit is ₹ 1. 20% of goods were lost, meaning 20 units were lost. Remaining goods are 100 – 20 = 80 units. These 80 units are sold at a profit of 50% on their cost. The cost of the 80 units is ₹ 80 (since cost per unit was ₹ 1). Selling price of these 80 units = Cost * (1 + Profit%) = ₹ 80 * (1 + 0.50) = ₹ 80 * 1.50 = ₹ 120. The businessman invested ₹ 100 initially (the cost of the total goods) and received ₹ 120 from the sale. The overall profit is ₹ 120 – ₹ 100 = ₹ 20. Overall profit percentage = (Overall Profit / Total Cost) * 100 = (₹ 20 / ₹ 100) * 100 = 20%.

– The profit/loss is calculated on the original total cost of the goods, even if a portion is lost.
– The selling price is calculated based on the goods that *are* sold, applying the given profit margin to their cost.
– Overall profit = Total Revenue – Total Cost.
– Overall profit percentage = (Overall Profit / Total Cost) * 100.

Setting the initial cost price to a convenient value like ₹ 100 simplifies calculations for percentage problems. The loss of goods means the cost invested in those goods is not recovered, and this must be accounted for in the overall profit calculation.

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