If two successive discounts of 50% and 10% are offered, what is the net discount (in %) ?

Options

A. 50
B. 55
C. 60
D. 65

Answer

To find the net discount when two successive discounts of 50% and 10% are offered, we can follow these steps:

1. **Assume the Initial Cost Price (CP)**:
Let's assume the initial cost price (CP) of the item is Rs. 100.

2. **Calculate the First Discount**:
The first discount is 50% of Rs. 100.
\[ \text{First Discount} = 50\% \text{ of } 100 = \frac{50}{100} \times 100 = Rs. 50 \]

3. **Calculate the Price After First Discount**:
Subtract the first discount from the initial CP:
\[ \text{Price after First Discount} = 100 - 50 = Rs. 50 \]

4. **Calculate the Second Discount**:
The second discount is 10% of the new price (Rs. 50).
\[ \text{Second Discount} = 10\% \text{ of } 50 = \frac{10}{100} \times 50 = Rs. 5 \]

5. **Calculate the Final Price After Both Discounts**:
Subtract the second discount from the price after the first discount:
\[ \text{Final Price} = 50 - 5 = Rs. 45 \]

6. **Calculate the Net Discount**:
The net discount can be calculated as the difference between the initial CP and the final price, expressed as a percentage of the initial CP:
\[ \text{Net Discount} = \left( \frac{100 - 45}{100} \right) \times 100 = 55\% \]

Thus, the net discount is **55%**.