A shopkeeper sells a refrigerators for Rs 22,000 and makes a profit of 10%. If he desires to make a profit of 18%, what should be his selling price?
Rs 23,600
To solve this problem, we need to find the new selling price that would give the shopkeeper an 18% profit, given he currently sells the refrigerator for Rs 22,000 and makes a 10% profit.
First, let's understand the components:
- Cost Price (CP): This is the actual price at which the shopkeeper bought the refrigerator. We need this to determine the new selling price (SP) for the desired profit percentage.
Let's find the Cost Price using the initial selling scenario:
- Initial Selling Price (SP1) = Rs 22,000
- Profit Percentage (P1) = 10%
Using the formula for profit, which is:
\(SP_1 = CP \times \left(1 + \frac{P_1}{100}\right)\)
Substituting the known values:
\(22,000 = CP \times \left(1 + \frac{10}{100}\right)\)
Simplify to find CP:
- \(22,000 = CP \times 1.1\)
- \(CP = \frac{22,000}{1.1} = 20,000\)
Now that we have the Cost Price as Rs 20,000, we can calculate the Selling Price for an 18% profit:
- Desired Profit Percentage (P2) = 18%
Using the same profit formula with the new profit percentage:
\(SP_2 = CP \times \left(1 + \frac{P_2}{100}\right)\)
Substituting the values:
\(SP_2 = 20,000 \times \left(1 + \frac{18}{100}\right)\)
Simplify this expression:
- \(SP_2 = 20,000 \times 1.18 = 23,600\)
Therefore, to achieve an 18% profit, the new selling price should be Rs 23,600.
This matches the given correct answer option.
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