Question

A man buys apples at a certain price per dozen and sells them at \emph{eight times that price per hundred}. What is his gain or loss percent?

• A. $4\%$ loss
• B. $8\frac{1}{4}$ loss
• C. $4\%$ gain
• D. $6\frac{1}{4}\%$ gain

Hint:

To compare prices quoted "per dozen'' and "per hundred,'' bring both CP and SP to the same lot size (e.g., 100 units). Ratios then simplify cleanly.

Answer 1

The Correct Option is A

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.
"Sells at eight times per hundred'' \Rightarrow\ 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 $=\dfrac{\text{Loss}}{\text{CP}}\times 100 =\dfrac{\frac{1}{3}C}{\frac{25}{3}C}\times 100=\dfrac{1}{25}\times 100=4\%$.
\[ \boxed{\text{Loss }=4\%} \]