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Sandeep sells an article at a loss of 10...

Sandeep sells an article at a loss of 10%. Had he bought it at 20% less and sold it for Rs. 55 more, he could have gained 40%. What is the cost price of the article?

A

Rs. 200

B

Rs. 225

C

Rs. 250

D

Rs. 275

Text Solution

AI Generated Solution

The correct Answer is:
To find the cost price of the article sold by Sandeep, we can follow these steps: ### Step 1: Define the Variables Let the cost price (CP) of the article be Rs. \( x \). ### Step 2: Calculate the Selling Price with a Loss of 10% Since Sandeep sells the article at a loss of 10%, the selling price (SP) can be calculated as: \[ SP = CP - \text{Loss} = x - 0.1x = 0.9x \] ### Step 3: Determine the New Cost Price with a 20% Reduction If Sandeep had bought the article at 20% less, the new cost price (CP2) would be: \[ CP2 = x - 0.2x = 0.8x \] ### Step 4: Calculate the New Selling Price with a Gain of 40% If he sold it for Rs. 55 more than the previous selling price, the new selling price (SP2) would be: \[ SP2 = 0.9x + 55 \] Given that this selling price results in a gain of 40%, we can express this as: \[ SP2 = CP2 + \text{Gain} = 0.8x + 0.4 \times 0.8x = 0.8x + 0.32x = 1.12x \] ### Step 5: Set Up the Equation Now we can set the two expressions for the new selling price equal to each other: \[ 0.9x + 55 = 1.12x \] ### Step 6: Solve for \( x \) Rearranging the equation gives: \[ 55 = 1.12x - 0.9x \] \[ 55 = 0.22x \] Now, solving for \( x \): \[ x = \frac{55}{0.22} = 250 \] ### Conclusion Thus, the cost price of the article is Rs. 250. ---
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