Question

What is the cost price of the article? I) The selling price of the article is Rs. \(50\).
II) The profit is \(10\%\).

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

To find cost price from selling price, profit percentage is also required.

Answer 1

The Correct Option is C

Concept:
If profit is \(r\%\), then \[ SP=CP\left(1+\frac{r}{100}\right) \] where \(SP\) is selling price and \(CP\) is cost price.

Step 1: Check Statement I. Statement I gives \[ SP=50 \] But profit percentage is not known. So cost price cannot be found. Thus Statement I alone is not sufficient.

Step 2: Check Statement II. Statement II gives \[ \text{Profit}=10\% \] But selling price is not known. So cost price cannot be found. Thus Statement II alone is not sufficient.

Step 3: Combine both statements. Using both statements, \[ SP=50,\qquad r=10 \] \[ 50=CP\left(1+\frac{10}{100}\right) \] \[ 50=CP\left(\frac{110}{100}\right) \] \[ 50=1.1CP \] \[ CP=\frac{50}{1.1} \] So the cost price can be uniquely found.

Step 4: Final answer. \[ \boxed{\text{Both statements together are sufficient, but neither alone is sufficient}} \]