Question

The profit earned by selling an article for Rs. 900 is double the loss incurred when sold for Rs. 490. At what price should it be sold to make 25% profit?

• A. Rs. 715
• B. Rs. 469
• C. Rs. 400
• D. Rs. 783.33

Hint:

Quick Tip: When a problem says “profit is double the loss,” directly form an equation using: \[ \text{Profit} = \text{SP} - \text{CP} \] \[ \text{Loss} = \text{CP} - \text{SP} \] Then solve for the Cost Price (CP) first. After finding CP, use: \[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \] to calculate the required selling price.

Answer 1

The Correct Option is D

Step 1: Let the loss when sold at Rs. 490 be \( L \). Then the profit when sold at Rs. 900 is \( 2L \), since the profit is double the loss. So \( 900 - \text{CP} = 2L \) and \( \text{CP} - 490 = L \).

Step 2: Add the two equations directly to eliminate CP: \[ (900 - \text{CP}) + (\text{CP} - 490) = 2L + L \] \[ 410 = 3L \implies L = \frac{410}{3} \]

Step 3: Substitute back to find the cost price: \[ \text{CP} = 490 + L = 490 + \frac{410}{3} = \frac{1470 + 410}{3} = \frac{1880}{3} \]

Step 4: Apply the 25% profit condition: \[ \text{SP} = \text{CP} \times 1.25 = \frac{1880}{3} \times \frac{5}{4} = \frac{9400}{12} = \frac{2350}{3} \] \[ \boxed{\text{SP} \approx \text{Rs. } 783.33} \]