By selling $12$ notebooks, the seller earns a profit equal to the \(\textit{selling price}\) of $2$ notebooks. What is his percentage profit?
By selling $12$ notebooks, the seller earns a profit equal to the \(\textit{selling price}\) of $2$ notebooks. What is his percentage profit?
Show Hint
When a statement compares profit to the \emph{selling price}, set up an equation with per-unit SP $S$ and CP $C$, then convert to profit% on CP at the end.
- $25\%$
- $20\%$
- $16\frac{2}{3}\%$
- Data inadequate
The Correct Option is B
Solution and Explanation
Step 1: Define per–unit prices.
Let the selling price per notebook be $S$ and the cost price per notebook be $C$.
Step 2: Translate the condition into an equation.
Profit on $12$ notebooks $=12(S-C)$. Given this equals SP of $2$ notebooks $=2S$:
\[ 12(S-C)=2S. \]
Step 3: Solve for $C$ in terms of $S$.
$12S-12C=2S \Rightarrow 10S=12C \Rightarrow C=\dfrac{5}{6}S$.
Step 4: Compute profit percent on cost.
Profit per notebook $=S-C=S-\dfrac{5}{6}S=\dfrac{1}{6}S$. Hence \[ \text{Profit\%}=\frac{\frac{1}{6}S}{\frac{5}{6}S}\times 100=\frac{1}{5}\times 100=20\%. \] \[ \boxed{20\%} \]
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