Questions :
An antique dealer sold three items, A, B, and C, with their selling prices in the ratio 3 : 4 : 5. He suffered a loss of 20% on item A, made a profit of 25% on item B, and broke even on item C. What was his exact percentage gain or loss in the overall deal?
Options :
- Loss of 0.42%
- Profit of 0.42%
- Profit of 1.42%
- Loss of 1.42%
correct answer : b)
Explanation :
Let the selling prices of items A, B, and C be 3x, 4x, and 5x respectively.
For item A, there is a loss of 20%, so:
CP of A = 3x × (100/80) = 3.75x
For item B, there is a profit of 25%, so:
CP of B = 4x × (100/125) = 3.2x
For item C, there is no profit or loss, so:
CP of C = 5x
Total Cost Price = 3.75x + 3.2x + 5x = 11.95x
Total Selling Price = 3x + 4x + 5x = 12x
Net Profit = 12x − 11.95x = 0.05x
Profit Percentage
= (0.05x / 11.95x) × 100
≈ 0.4184%
≈ 0.42%
Therefore, the dealer made an overall profit of 0.42%.
Hence, the correct answer is option (b) Profit of 0.42%. The options Loss of 0.42%, Profit of 1.42%, and Loss of 1.42% are incorrect because the overall selling price exceeds the overall cost price by only 0.05x, resulting in a profit of approximately 0.42%.