Question

If an item is sold for Rs.540 at a loss of 10%, then the cost price of the item is

• A. Rs.630.
• B. Rs.610.
• C. Rs.600.
• D. Rs.620.

Hint:

A 10% loss means the item is sold at 90% of its cost price.
If 90% of $CP$ is equal to 540, then 10% of $CP$ is $540 \div 9 = 60$.
Thus, 100% of $CP$ must be $60 \times 10 = 600$. This mental math method is incredibly fast!

Answer 1

The Correct Option is C

Step 1: Recall the loss formula.
When there is a loss: Selling Price = Cost Price x (1 - Loss% / 100). Here SP = Rs.540 and Loss = 10%.
Step 2: Substitute and solve.
\[ 540 = CP \times \frac{90}{100} \] \[ CP = \frac{540 \times 100}{90} = \frac{54000}{90} = 600 \]
Step 3: Verify.
Loss = 600 - 540 = Rs.60, which is exactly 10% of Rs.600. Correct! \[ \boxed{Rs.600} \]