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A retailer selling mangoes offered a flat discount of 10% on his marked price. Further, owing to persistent bargaining by a customer, he offered n mangoes free for every 12 mangoes purchased by the customer and still made an overall profit of 20% in the transaction. Find the value of n, if the mangoes were marked at more than their cost price.

Question

A retailer selling mangoes offered a flat discount of 10% on his marked price. Further, owing to persistent bargaining by a customer, he offered n mangoes free for every 12 mangoes purchased by the customer and still made an overall profit of 20% in the transaction. Find the value of n, if the mangoes were marked at more than their cost price.

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Solution

Let's solve this step by step:

Step 1: Let's assume the cost price of each mango is 1.Therefore,thecostpriceof12mangoesis1. Therefore, the cost price of 12 mangoes is 12.

Step 2: The retailer is selling the mangoes at a 10% discount on the marked price. Let's assume the marked price of each mango is x.Therefore,thesellingpriceofeachmangoisx. Therefore, the selling price of each mango is 0.9x and the selling price of 12 mangoes is $10.8x.

Step 3: The retailer is also offering n mangoes free for every 12 mangoes purchased. Therefore, the cost price of (12+n) mangoes is $(12+n).

Step 4: The retailer is making a 20% profit on the transaction. Therefore, the selling price of (12+n) mangoes is 1.2 times the cost price of (12+n) mangoes. So, 10.8x=1.210.8x = 1.2 * (12+n).

Step 5: Solving the equation from step 4 gives us x = 1.2 * (12+n) / 10.8.

Step 6: Since the mangoes were marked at more than their cost price, x > 1. Substituting the value of x from step 5 gives us 1.2 * (12+n) / 10.8 > 1.

Step 7: Solving the inequality from step 6 gives us n > 0.8.

Therefore, the retailer is offering at least one mango free for every 12 mangoes purchased.

This problem has been solved

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