Multiple choice

Discounts offered by the fruit vendor on the selling price of mangoes are in the following way. 5% discount on the selling price of 1 dozen mangoes 10% discount on the selling price of 2 dozen mangoes 15% discount on the selling price of 3 dozen mangoes and so on. Find the maximum percentage discount a fruit vendor can give to a customer so as to have no loss. (Note: A fruit vendor gets 25% profit on selling 1 dozen mangoes without giving discount)

  1. 25%

  2. 15%

  3. 20%

  4. 36%

  5. 28%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A 25% profit on cost means the selling price is 1.25 times the cost. To have no loss, the discounted selling price must equal the cost price, meaning the discount must be 20% of the original selling price (since 1.25 * 0.8 = 1.0). The pattern of discounts provided is irrelevant to finding the maximum possible discount that avoids a loss.

AI explanation

Let the cost price of 1 dozen mangoes be 100 rupees. Given the 25% profit on 1 dozen without a discount, the selling price is 125 rupees. The maximum successive discounts given follow the pattern 5%, 10%, and 15%, and using the successive discount formula for these three gives 1 minus 0.95 times 0.90 times 0.85, which equals 0.27425, meaning the price falls to 72.575% of its original value. Applying the full 20% discount instead makes the selling price 125 times 0.80, which equals 100 rupees. The maximum percentage discount the fruit vendor can give to have no loss is 20%.

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