Question : A man purchased some oranges at the rate of 3 for Rs. 40 and the same quantity at 5 for Rs. 60. If he sells all the oranges at the rate of 3 for Rs. 50, find his gain or loss percentage (to the nearest integer).
Option 1: 32% profit
Option 2: 31% loss
Option 3: 34% loss
Option 4: 31% profit
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Correct Answer: 32% profit
Solution :
Let the man purchase 15 oranges of each type (least common multiple of 3 and 5).
The cost price of the first type = $\frac{40}{3}×15=200$
The cost price of the second type = $\frac{60}{5}×15=180$
The total cost price = 200 + 180 = 380
The total selling price = $\frac{50}{3}×30=500$
So,
Profit percentage = $\frac{\text{Selling price}-\text{Cost price}}{\text{Cost price}}×100$
= $\frac{500-380}{380}×100$
= $\frac{120}{380}×100$
= $\frac{600}{19}$
= $31.58\% \approx 32\%$
Hence, the answer is 32% profit.
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