The marked price of a pen is Rs 3000. the shopkeeper gives two successive discounts of 15% and a% to the customer. If the customer pays Rs 2142 for the pen, then what is the value (in percentage) of a?

Options

A. 16
B. 14
C. 18
D. 17

Answer

To solve the problem step by step, we will use the concept of successive discounts and the formula for calculating the selling price after applying discounts.

### Step-by-Step Solution:

1. **Identify the Marked Price (MP)**:
- The marked price of the pen is given as Rs 3000.

2. **Calculate the Selling Price after the First Discount**:
- The first discount is 15%.
- The selling price (SP) after the first discount can be calculated using the formula:
\[ SP_1 = MP \times \left(1 - \frac{D_1}{100}\right) \]
- Here, \(D_1 = 15\%\).
- Thus,
\[ SP_1 = 3000 \times \left(1 - \frac{15}{100}\right) = 3000 \times \left(\frac{85}{100}\right) = 3000 \times 0.85 = 2550 \]

3. **Calculate the Selling Price after the Second Discount**:
- Let the second discount be \(a\%\).
- The selling price after the second discount can be calculated as:
\[ SP = SP_1 \times \left(1 - \frac{a}{100}\right) \]
- We know the final selling price (SP) is Rs 2142.
- Therefore,
\[ 2142 = 2550 \times \left(1 - \frac{a}{100}\right) \]

4. **Rearranging the Equation**:
- To find \(a\), we first isolate \(1 - \frac{a}{100}\):
\[ 1 - \frac{a}{100} = \frac{2142}{2550} \]

5. **Calculate the Right Side**:
- Now, we simplify \(\frac{2142}{2550}\):
\[ \frac{2142}{2550} = 0.84 \]
- Thus,
\[ 1 - \frac{a}{100} = 0.84 \]

6. **Finding \(a\)**:
- Now, we can solve for \(a\):
\[ \frac{a}{100} = 1 - 0.84 = 0.16 \]
- Therefore,
\[ a = 0.16 \times 100 = 16 \]

7. **Conclusion**:
- The value of \(a\) is 16%.