A man buys apples at a certain price per dozen and sells them at eight times that price per hundred. What is his gain or loss percent?
A man buys apples at a certain price per dozen and sells them at eight times that price per hundred. What is his gain or loss percent?
Show Hint
- $4\%$ loss
- $8\frac{1}{4}$ loss
- $4\%$ gain
- $6\frac{1}{4}\%$ gain
The Correct Option is A
Solution and Explanation
Step 1: Set up comparable lots.
Let the cost price be ₹ $C$ per dozen.
Then CP per $100$ apples $=\dfrac{100}{12}\,C=\dfrac{25}{3}C$.
Step 2: Interpret the selling condition.
$\text{"Sells at eight times per hundred''}$ $\Rightarrow$ $\text{selling price per 100 apples}=8C. $
Step 3: Compute gain/loss percent on a $100$-apple lot.
Profit (or loss) $= \text{SP}-\text{CP}=8C-\dfrac{25}{3}C=\left(8-\dfrac{25}{3}\right)C=-\dfrac{1}{3}C$.
Loss percent $=\dfrac{\text{Loss}}{\text{CP}}\times 100 =\dfrac{\frac{1}{3}C}{\frac{25}{3}C}\times 100=\dfrac{1}{25}\times 100=4\%$.
\[ \boxed{\text{Loss }=4\%} \]
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