Question

Selling at Rs.1140 gives 5% loss. Find SP for 5% profit.

• A. Rs.1200
• B. Rs.1230
• C. Rs.1260
• D. Rs.1290

Hint:

Remember the relationships:
- Loss: SP = CP \(\times\) (100 - Loss%)/100
- Profit: SP = CP \(\times\) (100 + Profit%)/100
These allow you to quickly move between CP and SP given a percentage loss or profit.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem requires finding the Cost Price (CP) from a given selling price (SP) and loss percentage, and then calculating a new selling price (SP') to achieve a specified profit percentage.

Step 2: Key Formula or Approach:
1. If SP and Loss% are known: CP = $\frac{\text{SP}}{1 - \frac{\text{Loss %}}{100}}$
2. If CP and Profit% are known: SP' = CP \(\times\) $\left(1 + \frac{\text{Profit %}}{100}\right)$

Step 3: Detailed Explanation:
Given:
- Selling Price (SP) = Rs. 1140.
- Loss Percentage = 5%.
- Desired Profit Percentage = 5%.
Part 1: Calculate the Cost Price (CP)
If there is a 5% loss, it means SP is 95% of CP.
\[ \text{SP} = \text{CP} \times \left(1 - \frac{5}{100}\right) = \text{CP} \times 0.95 \]
\[ 1140 = \text{CP} \times 0.95 \]
\[ \text{CP} = \frac{1140}{0.95} \]
\[ \text{CP} = \text{Rs. } 1200 \]
Part 2: Calculate the new Selling Price (SP') for 5% profit
Desired profit is 5%, so SP' will be 105% of CP.
\[ \text{SP'} = \text{CP} \times \left(1 + \frac{5}{100}\right) = \text{CP} \times 1.05 \]
\[ \text{SP'} = 1200 \times 1.05 \]
\[ \text{SP'} = 1260 \]

Step 4: Final Answer:
The article should be sold for Rs. 1260 to make a 5% profit.

Answer 2

Since CP is the single number connecting both the loss scenario and the profit scenario, each candidate new selling price can be tested by computing the CP it implies, then checking whether that same CP produces a 5% loss when sold at Rs. 1140.

1. Rs. 1200: If this were the answer at 5% profit, CP would be \( \frac{1200}{1.05} \approx 1142.86 \). A 5% loss on this CP would mean selling at \( 1142.86 \times 0.95 \approx 1085.71 \), not Rs. 1140, so this does not fit.
2. Rs. 1230: This would imply CP \( = \frac{1230}{1.05} \approx 1171.43 \). A 5% loss on this CP gives \( 1171.43 \times 0.95 \approx 1112.86 \), still not matching Rs. 1140.
3. Rs. 1260: This implies CP \( = \frac{1260}{1.05} = 1200 \). Checking the loss condition: 5% loss on CP of 1200 gives \( 1200 \times 0.95 = 1140 \), exactly matching the given selling price for the loss scenario.
4. Rs. 1290: This implies CP \( = \frac{1290}{1.05} \approx 1228.57 \). A 5% loss on this CP gives \( 1228.57 \times 0.95 \approx 1167.14 \), which does not match Rs. 1140 either.

Only Rs. 1260, worked backward to a CP of Rs. 1200, is consistent with both the given loss scenario and the required profit scenario at once.

Therefore, the correct answer is Rs. 1260.