Multiple choice

Ramesh had 180 toys in his shop all of which he bought at the same price. On a particular day, he could sell 20% of the toys at a profit of 20% and 30% of the toys at a profit of 30%. What is the maximum percent of loss he could in on the remaining toys so that he doesn't incur a loss overall?

  1. 26

  2. 28

  3. 25

  4. 22
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A Correct answer
Explanation

The first two groups produce revenue equal to 36 x 1.2 + 54 x 1.3 = 113.4 cost units. The remaining 90 toys can produce 66.6 units without an overall loss, which is 74% of their cost, so the maximum loss is 26%.

AI explanation

Assume the cost price of each toy is Rs. 1, making the total cost for the 180 toys Rs. 180. He sells 20% of the toys (36 toys) at a 20% profit, earning 36 * 1.2 = Rs. 43.2, and 30% of the toys (54 toys) at a 30% profit, earning 54 * 1.3 = Rs. 70.2. The total revenue from these sales is 43.2 + 70.2 = Rs. 113.4, meaning he must sell the remaining 90 toys for at least 180 - 113.4 = Rs. 66.6 to avoid a loss. The required selling price per remaining toy is 66.6 / 90 = Rs. 0.74, resulting in a loss percentage of ((1 - 0.74) / 1) * 100 = 26%.

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