Question

By selling 18 articles, a shopkeeper earns the cost price of 24 articles. By what percent should he increase the selling price so that by selling 24 articles, he earns the cost price of 36 articles?

• A. 10\%
• B. 20\%
• C. 12.5\%
• D. 25\%

Hint:

Translate statements like "selling $n$ items earns cost of $m$ items" into ratios: \(\frac{SP}{CP}=\frac{m}{n}\). Then compare ratios to get the required percent change.

Answer 1

The Correct Option is C

Step 1: Current selling price to cost price ratio. 
From \(18\,SP = 24\,CP\) \(\Rightarrow\) \(\frac{SP}{CP}=\frac{24}{18}=\frac{4}{3}\). 

Step 2: Required ratio. 
We want \(24\,SP_{\text{new}}=36\,CP \Rightarrow \frac{SP_{\text{new}}}{CP}=\frac{36}{24}=\frac{3}{2}\). 

Step 3: Percentage increase in SP. 
\[ \%\text{ increase}=\frac{SP_{\text{new}}-SP}{SP}\times 100 =\frac{\tfrac{3}{2}-\tfrac{4}{3}}{\tfrac{4}{3}}\times 100 =\frac{\tfrac{1}{6}}{\tfrac{4}{3}}\times 100 =\frac{1}{6}\cdot\frac{3}{4}\times 100 =12.5\%. \] \[ \boxed{12.5\%} \]