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

Answer 2

Assuming a convenient cost price of Rupees 1 per article turns the ratio relationships into simple selling prices that are easy to check.

1. 10%: A 10% increase on the original selling price of \(4/3\) gives \(\dfrac{4}{3}\times1.10\approx1.467\), which is not \(1.5\), the price needed for the new condition.
2. 20%: A 20% increase gives \(\dfrac{4}{3}\times1.20=1.6\), overshooting the required \(1.5\).
3. 12.5%: A 12.5% increase gives \(\dfrac{4}{3}\times1.125=1.5\), matching exactly.
4. 25%: A 25% increase gives \(\dfrac{4}{3}\times1.25\approx1.667\), overshooting the required \(1.5\) by a wide margin.

With cost price taken as Rupees 1 per article, selling 18 articles for the cost of 24 means the original selling price per article is \(24/18=4/3\). To sell 24 articles for the cost of 36, the new selling price per article must be \(36/24=1.5\). The percentage increase from \(4/3\) to \(1.5\) is \(\dfrac{1.5-4/3}{4/3}\times100=12.5\%\).

So the correct answer is 12.5%.