The marked price of an article is ₹3,600. Two sucessive discounts of x% and 15% are offered on it during a sale. If the selling price of the article is ₹2,448, then the value of x is:

Options

A. 25
B. 18
C. 20
D. 10

Answer

To solve the problem, we need to find the value of x given the marked price, the selling price, and the successive discounts.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Marked Price (MP) = ₹3,600
- Selling Price (SP) = ₹2,448
- Second Discount = 15%
- First Discount = x%

2. **Apply the First Discount:**
The selling price after the first discount (x%) can be calculated as:
\[ SP_1 = MP \times \left(1 - \frac{x}{100}\right) \]
where \( SP_1 \) is the price after the first discount.

3. **Apply the Second Discount:**
After applying the second discount of 15% on \( SP_1 \), the selling price becomes:
\[ SP = SP_1 \times \left(1 - \frac{15}{100}\right) \]
Substituting \( SP_1 \) from the previous step:
\[ SP = MP \times \left(1 - \frac{x}{100}\right) \times \left(1 - 0.15\right) \]

4. **Substitute the Values:**
Now, substituting the known values into the equation:
\[ 2448 = 3600 \times \left(1 - \frac{x}{100}\right) \times 0.85 \]

5. **Simplify the Equation:**
First, calculate \( 3600 \times 0.85 \):
\[ 3600 \times 0.85 = 3060 \]
Now the equation becomes:
\[ 2448 = 3060 \times \left(1 - \frac{x}{100}\right) \]

6. **Isolate the Discount Factor:**
Divide both sides by 3060:
\[ \frac{2448}{3060} = 1 - \frac{x}{100} \]
Calculate \( \frac{2448}{3060} \):
\[ \frac{2448}{3060} = 0.8 \]
So, we have:
\[ 0.8 = 1 - \frac{x}{100} \]

7. **Solve for x:**
Rearranging gives:
\[ \frac{x}{100} = 1 - 0.8 = 0.2 \]
Therefore:
\[ x = 0.2 \times 100 = 20 \]

8. **Final Answer:**
The value of x is **20%**.