A businessman sold 45% of his stock at a gain of 20% and the rest at a gain of…
2024
A businessman sold 45% of his stock at a gain of 20% and the rest at a gain of 15%. The overall percentage of gain to the businessman?
- A.
23%
- B.
19%
- C.
21%
- D.
17%
Attempted by 2 students.
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Correct answer: D
The overall percentage gain when different portions of a quantity are sold at different individual gain rates equals the weighted average of those gain rates, where each rate is weighted by the share (fraction) of the total stock it applies to -- not a simple average of the rates.
Assume the total cost value of the stock is 100 units.
The 45% portion is sold at a 20% gain, contributing 45 times 20 percent = 9 (percentage points of the total cost value).
The remaining 55% portion is sold at a 15% gain, contributing 55 times 15 percent = 8.25 (percentage points of the total cost value).
Adding the two contributions gives the overall gain: 9 + 8.25 = 17.25%, which rounds to the closest offered option, 17%.
Cross-check using total revenue: revenue from the 45% portion = 45 times 1.20 = 54; revenue from the 55% portion = 55 times 1.15 = 63.25; total revenue = 117.25 against a total cost of 100, confirming an overall gain of 17.25% (approximately 17%), matching the same result.