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: Understanding the Question:
The problem has two parts: first, finding the cost price (CP) of an article based on given profit and loss scenarios. Second, calculating the selling price (SP) required to achieve a 25% profit on that CP.

Step 2: Key Formula or Approach:
1. Profit = SP - CP
2. Loss = CP - SP
3. To make P% profit: SP = CP \(\times\) $\left(1 + \frac{P}{100}\right)$

Step 3: Detailed Explanation:
Let the Cost Price (CP) of the article be Rs. \( x \).
Scenario 1: Selling for Rs. 900
Selling Price (SP1) = Rs. 900.
Profit = SP1 - CP = $900 - x$.
Scenario 2: Selling for Rs. 490
Selling Price (SP2) = Rs. 490.
Loss = CP - SP2 = $x - 490$.
Given Relationship:
The profit earned is double the loss incurred.
\[ 900 - x = 2 \times (x - 490) \]
\[ 900 - x = 2x - 980 \]
Rearrange the equation to solve for \( x \):
\[ 900 + 980 = 2x + x \]
\[ 1880 = 3x \]
\[ x = \frac{1880}{3} \]
CP = Rs. $\frac{1880}{3}$.
Calculate Selling Price for 25% Profit:
Desired profit = 25% = 0.25.
\[ \text{SP for 25\% profit} = \text{CP} \times (1 + 0.25) = \text{CP} \times 1.25 \]
\[ \text{SP} = \frac{1880}{3} \times 1.25 \]
\[ \text{SP} = \frac{1880}{3} \times \frac{5}{4} \]
\[ \text{SP} = \frac{1880 \times 5}{12} \]
\[ \text{SP} = \frac{9400}{12} = \frac{2350}{3} \]
\[ \text{SP} = 783.33 \]