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 both percentages here are measured against the same cost price, we do not need to calculate the cost price separately. A loss of 5% means the given selling price is 95% of the cost price, and a profit of 5% means the new selling price must be 105% of the same cost price, so the new price is simply the old price scaled by the ratio 105:95. We can check each option against this ratio.

1. Rs. 1200: Scaling Rs. 1140 by \( \frac{105}{95} \) does not come out to this value, so it does not match the required scale.
2. Rs. 1230: This value is also not what results from scaling 1140 by \( \frac{105}{95} \), so it does not satisfy the ratio.
3. Rs. 1260: Scaling gives \( 1140 \times \frac{105}{95} = 1140 \times \frac{21}{19} \). Since \( 1140 \div 19 = 60 \), this becomes \( 60 \times 21 = 1260 \), which matches exactly.
4. Rs. 1290: This does not equal \( 1140 \times \frac{21}{19} \) either, so it does not fit the required scaling.

Only Rs. 1260 is in the correct proportion to Rs. 1140 for turning a 5% loss into a 5% profit on the same cost price.

Therefore, the correct answer is Rs. 1260.