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: Express both selling prices as a percentage of the same cost price.
A 5% loss means the given selling price is 95% of the cost price, so \( \text{SP} = 0.95 \times \text{CP} \). A 5% profit means the new selling price is 105% of the same cost price, so \( \text{SP}' = 1.05 \times \text{CP} \).

Step 2: Divide the two to remove the cost price entirely.
\[ \frac{\text{SP}'}{\text{SP}} = \frac{1.05 \times \text{CP}}{0.95 \times \text{CP}} = \frac{105}{95} = \frac{21}{19} \]

Step 3: Apply this ratio directly to the given selling price.
\[ \text{SP}' = 1140 \times \frac{21}{19} \] Since \( 1140 \div 19 = 60 \), \[ \text{SP}' = 60 \times 21 = \boxed{1260} \]