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

Answer: (A)

Rs. 200

Answer 2

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.