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.
\[ \text{SP for 25\% profit} = \text{CP} \times (1 + 0.25) = \text{CP} \times 1.25 \]
\[ \text{SP} = \frac{1880}{3} \times 1.25 \]
\[ \text{SP} = \frac{1880}{3} \times \frac{5}{4} \]
\[ \text{SP} = \frac{1880 \times 5}{12} \]
\[ \text{SP} = \frac{9400}{12} = \frac{2350}{3} \]
\[ \text{SP} = 783.33 \]

Answer 2

Instead of forming the algebraic equation directly, we can work backwards from each candidate selling price: assume it is the correct 25% profit price, derive the cost price it implies, and check whether that cost price is consistent with the given relationship, that selling at Rs. 900 gives a profit exactly double the loss from selling at Rs. 490.

1. Rs. 715: If Rs. 715 gives a 25% profit, the cost price would be \( \frac{715}{1.25} = 572 \). Checking this against the given condition, the profit at Rs. 900 would be \( 900 - 572 = 328 \), and the loss at Rs. 490 would be \( 572 - 490 = 82 \). Since \( 328 \neq 2 \times 82 = 164 \), this cost price does not satisfy the condition, so this option is inconsistent.
2. Rs. 469: This would imply a cost price of \( \frac{469}{1.25} = 375.2 \). But a cost price below Rs. 490 would mean selling at Rs. 490 produces a profit, not the loss the question describes, so this option contradicts the problem's setup entirely.
3. Rs. 400: This would imply a cost price of \( \frac{400}{1.25} = 320 \), which is also below Rs. 490 and again would turn the described loss into a profit, so this option is inconsistent with the given scenario as well.
4. Rs. 783.33: This implies a cost price of \( \frac{783.33}{1.25} \approx 626.67 \). Checking the condition, the profit at Rs. 900 is \( 900 - 626.67 = 273.33 \), and the loss at Rs. 490 is \( 626.67 - 490 = 136.67 \). Since \( 273.33 \approx 2 \times 136.67 \), the profit is indeed double the loss, so this cost price satisfies the given condition exactly.

Only the cost price implied by Rs. 783.33 satisfies both the profit-loss relationship and the requirement of lying between Rs. 490 and Rs. 900.

Therefore, the correct answer is Rs. 783.33.