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A businessman bought an article and sold...

A businessman bought an article and sold it at a loss of 5%. If he had bought it for 10% less and sold it for 33 more, he would have had a profit of 30%. Find the cost price of this article.

A

a)Rs 330

B

b) Rs 155

C

c) Rs 150

D

d)Rs 300

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's denote the cost price (CP) of the article as \( x \). ### Step 1: Determine the Selling Price (SP) at a Loss of 5% When the businessman sells the article at a loss of 5%, the selling price can be calculated as follows: \[ SP = CP - (5\% \text{ of } CP) = x - 0.05x = 0.95x \] ### Step 2: Calculate the New Cost Price with 10% Reduction If the businessman had bought the article for 10% less, the new cost price would be: \[ \text{New CP} = x - (10\% \text{ of } x) = x - 0.10x = 0.90x \] ### Step 3: Determine the Selling Price for a Profit of 30% If he sold it for 33 more than the new cost price and made a profit of 30%, the selling price can be calculated as: \[ \text{Profit} = 30\% \text{ of New CP} = 0.30 \times 0.90x = 0.27x \] Thus, the selling price in this scenario would be: \[ SP = \text{New CP} + \text{Profit} = 0.90x + 0.27x = 1.17x \] ### Step 4: Set Up the Equation According to the problem, the selling price in this scenario is also equal to the original selling price plus 33: \[ 1.17x = 0.95x + 33 \] ### Step 5: Solve the Equation Now we can solve for \( x \): \[ 1.17x - 0.95x = 33 \] \[ 0.22x = 33 \] \[ x = \frac{33}{0.22} = 150 \] ### Conclusion The cost price of the article is \( \text{Rs. } 150 \).
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