An article is marked at Rs. 5,000. The shopkeeper allows successive discounts of x%, y%, z% on it. The net selling price is

Options

A. Rs `((100-x)(100+y)(100+z))/(200)`
B. Rs `((100+x)(100+y)(100-z))/(200)`
C. Rs `((100-x)(100-y)(100-z))/(200)`
D. Rs `((100-x)(100+y)(100-z))/(200)`

Answer

To find the net selling price of an article after successive discounts, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Marked Price**:
The article is marked at Rs. 5000.

2. **Understand Successive Discounts**:
The shopkeeper gives successive discounts of x%, y%, and z%. This means that after each discount, the new price becomes the base for the next discount.

3. **Calculate the Selling Price After Each Discount**:
- After the first discount of x%, the selling price (SP1) can be calculated as:
\[ SP1 = \text{Marked Price} \times \left(1 - \frac{x}{100}\right) = 5000 \times \left(1 - \frac{x}{100}\right) \]
- After the second discount of y%, the selling price (SP2) becomes:
\[ SP2 = SP1 \times \left(1 - \frac{y}{100} \right) = 5000 \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{y}{100}\right) \]
- After the third discount of z%, the final selling price (SP3) is:
\[ SP3 = SP2 \times \left(1 - \frac{z}{100} \right) = 5000 \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{y}{100}\right) \times \left(1 - \frac{z}{100}\right) \]

4. **Simplifying the Expression**:
- The final selling price can be expressed as:
\[ SP = 5000 \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{y}{100}\right) \times \left(1 - \frac{z}{100}\right) \]
- This can also be written as:
\[ SP = \frac{5000 \times (100 - x)(100 - y)(100 - z)}{100^3} \]

5. **Final Result**:
- Therefore, the net selling price after the successive discounts is:
\[ SP = \frac{5000 \times (100 - x)(100 - y)(100 - z)}{100^3} \]