A watch is sold at a profit of 20%. If both the cost price and selling price are reduced by Rs.100, then the profit would be 5% more. Find the original cost price of the watch.
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A.
Rs.550
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B.
Rs.450
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C.
Rs.600
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D.
Rs.500
Correct Answer:
D. Rs.500
Explanation:
Explanation
The original profit is 20%. If both the cost price (CP) and selling price (SP) are reduced by Rs. 100, the profit percentage increases by 5%, making the new profit 25%. Since the reduction in both CP and SP is the same, the absolute profit (SP - CP) remains constant, but it is now calculated against a lower cost price, resulting in a higher percentage.
Step-By-Step Solution - Step 1. Define the original variables. Let the original Cost Price be CP. Since the profit is 20%, the original Selling Price (SP) is 120% of CP, or 1.2CP.
- Step 2. Define the new variables. The new Cost Price is CP - 100 and the new Selling Price is 1.2CP - 100.
- Step 3. Set up the equation using the new profit percentage. The new profit is 25%, so the new SP must equal 125% of the new CP: 1.2CP - 100 = 1.25(CP - 100).
- Step 4. Expand the equation: 1.2CP - 100 = 1.25CP - 125.
- Step 5. Solve for CP by isolating the variable: 125 - 100 = 1.25CP - 1.2CP. This simplifies to 25 = 0.05CP.
- Step 6. Calculate the final value: CP = 25 / 0.05 = 500. The original cost price of the watch is Rs. 500.
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