A shopkeeper buys mangoes at the price of 6 rupee a dozen. During transportation, 20% of the mangoes get destroyed. At what price must he sell the mangoes if he wants to realise a profit of 60%?
Question
A shopkeeper buys mangoes at the price of 6 rupee a dozen. During transportation, 20% of the mangoes get destroyed. At what price must he sell the mangoes if he wants to realise a profit of 60%?
Solution
Sure, let's break it down:
Step 1: Calculate the cost price of the mangoes The shopkeeper buys mangoes at 6 rupees per dozen. This means the cost price of one mango is 6/12 = 0.5 rupees.
Step 2: Calculate the loss due to transportation During transportation, 20% of the mangoes get destroyed. This means for every dozen, the shopkeeper only has 12 - (20/100 * 12) = 9.6 mangoes.
Step 3: Adjust the cost price considering the loss Since the shopkeeper effectively only has 9.6 mangoes per dozen after accounting for the loss, the cost price per mango increases. The new cost price per mango is 6/9.6 = 0.625 rupees.
Step 4: Calculate the selling price for a profit of 60% The shopkeeper wants to realise a profit of 60%. This means the selling price should be 160% of the cost price. So, the selling price per mango should be 160/100 * 0.625 = 1 rupee.
Therefore, the shopkeeper must sell the mangoes at 1 rupee each to realise a profit of 60%.
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