An article is sold for rupees 642.60 after successive discount of 15% and 10%. What is the market price of the article?

Options

A. Rs 840
B. Rs 800
C. Rs 820
D. Rs 880

Answer

To find the market price of the article after successive discounts of 15% and 10%, we can follow these steps:

### Step 1: Understand the Discounts
The article has two successive discounts:
- First discount: 15%
- Second discount: 10%

### Step 2: Calculate the Effective Discount
To find the effective discount percentage when applying two successive discounts, we can use the formula:
\[ \text{Effective Discount} = A + B - \frac{A \times B}{100} \]
where \( A \) is the first discount (15%) and \( B \) is the second discount (10%).

Substituting the values:
\[ \text{Effective Discount} = 15 + 10 - \frac{15 \times 10}{100} \]
Calculating the product:
\[ \frac{15 \times 10}{100} = 1.5 \]
Now substituting back:
\[ \text{Effective Discount} = 15 + 10 - 1.5 = 23.5\% \]

### Step 3: Relate Selling Price to Market Price
Let the market price (MP) of the article be \( x \). After applying the effective discount of 23.5%, the selling price (SP) is given as Rs. 642.60. This can be expressed as:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Effective Discount}}{100}\right) \]
Substituting the values:
\[ 642.60 = x \times \left(1 - \frac{23.5}{100}\right) \]
This simplifies to:
\[ 642.60 = x \times 0.765 \]

### Step 4: Solve for Market Price
To find \( x \), we rearrange the equation:
\[ x = \frac{642.60}{0.765} \]
Calculating this gives:
\[ x \approx 840 \]

### Conclusion
The market price of the article is approximately Rs. 840.

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