Question

A man sells an article at 5\(\%\) profit. If he had bought it at 5\(\%\) less and sold it for Re. 1 less, he would have gained 10\(\%\). The cost price of the article is

• A. Rs. 200
• B. Rs. 150
• C. Rs. 250
• D. Rs. 240

Answer 1

The Correct Option is A

The correct option is (A): 200
Explanation:Let the cost price of the article be \( x \).
Given that he sells the article at a 5% profit, the selling price (SP) can be expressed as:
\[\text{SP} = x + 0.05x = 1.05x\]
If he had bought it at 5% less, the new cost price would be:
\[\text{New Cost Price} = x - 0.05x = 0.95x\]
He sells it for Re. 1 less, so the new selling price is:
\[\text{New SP} = 1.05x - 1\]
According to the problem, this new selling price gives him a 10% profit on the new cost price:
\[\text{New SP} = 0.95x + 0.10(0.95x) = 0.95x + 0.095x = 1.045x\]
Setting the two expressions for the new selling price equal to each other:
\[1.05x - 1 = 1.045x\]
Now, solving for \( x \):
\[1.05x - 1.045x = 1\]
\[0.005x = 1\]
\[x = \frac{1}{0.005} = 200\]
Thus, the cost price of the article is Option A: Rs. 200.