Question:
A Television was sold at \(30\%\) profit. If it had been sold for Rs.1000 more, then the profit would have been \(40\%\). The cost of Television in rupees is
A Television was sold at \(30\%\) profit. If it had been sold for Rs.1000 more, then the profit would have been \(40\%\). The cost of Television in rupees is
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If profit percentage changes and the selling price difference is given, directly equate the profit difference to the price difference.
Updated On: Jul 15, 2026
- \(9500\)
- \(10000\)
- \(12000\)
- \(15000\)
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The Correct Option is B
Solution and Explanation
Concept:
The difference in selling prices equals the difference in profit percentages.
Step 1: Assume cost price.
Let the cost price be: \[ x \] At \(30\%\) profit: \[ SP_1=130\%\text{ of }x \] \[ =\frac{130x}{100} \] At \(40\%\) profit: \[ SP_2=140\%\text{ of }x \] \[ =\frac{140x}{100} \]
Step 2: Use the given condition.
Difference in selling price: \[ SP_2-SP_1=1000 \] So: \[ \frac{140x}{100}-\frac{130x}{100}=1000 \] \[ \frac{10x}{100}=1000 \] \[ \frac{x}{10}=1000 \]
Step 3: Solve for \(x\).
\[ x=10000 \] Thus, the cost price of the television is: \[ \boxed{10000} \]
Step 1: Assume cost price.
Let the cost price be: \[ x \] At \(30\%\) profit: \[ SP_1=130\%\text{ of }x \] \[ =\frac{130x}{100} \] At \(40\%\) profit: \[ SP_2=140\%\text{ of }x \] \[ =\frac{140x}{100} \]
Step 2: Use the given condition.
Difference in selling price: \[ SP_2-SP_1=1000 \] So: \[ \frac{140x}{100}-\frac{130x}{100}=1000 \] \[ \frac{10x}{100}=1000 \] \[ \frac{x}{10}=1000 \]
Step 3: Solve for \(x\).
\[ x=10000 \] Thus, the cost price of the television is: \[ \boxed{10000} \]
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