An article is sold for Rs. 1,683 , after giving three successive discounts of `15%,10%and12%` on its marked price .The marked price of the article is :

Options

A. Rs. 2,400
B. Rs. 2,640
C. Rs. 2,500
D. Rs. 2,560

Answer

To find the marked price (MP) of an article sold for Rs. 1,683 after three successive discounts of 15%, 10%, and 12%, we can follow these steps:

### Step 1: Understand the formula for successive discounts
When successive discounts are applied, the selling price (SP) can be calculated using the formula:
\[ SP = MP \times \left(\frac{100 - A}{100}\right) \times \left(\frac{100 - B}{100}\right) \times \left(\frac{100 - C}{100}\right) \]
where A, B, and C are the percentages of the discounts.

### Step 2: Substitute the discount values
In our case:
- A = 15%
- B = 10%
- C = 12%

Thus, we can substitute these values into the formula:
\[ SP = MP \times \left(\frac{100 - 15}{100}\right) \times \left(\frac{100 - 10}{100}\right) \times \left(\frac{100 - 12}{100}\right) \]
This simplifies to:
\[ SP = MP \times \left(\frac{85}{100}\right) \times \left(\frac{90}{100}\right) \times \left(\frac{88}{100}\right) \]

### Step 3: Set up the equation with the selling price
We know that the selling price (SP) is Rs. 1,683. Therefore, we can write:
\[ 1683 = MP \times \left(\frac{85}{100}\right) \times \left(\frac{90}{100}\right) \times \left(\frac{88}{100}\right) \]

### Step 4: Calculate the product of the fractions
First, calculate the product of the fractions:
\[ \frac{85}{100} \times \frac{90}{100} \times \frac{88}{100} = \frac{85 \times 90 \times 88}{100 \times 100 \times 100} \]
Calculating the numerator:
\[ 85 \times 90 = 7650 \]
\[ 7650 \times 88 = 673200 \]
So, the product becomes:
\[ \frac{673200}{1000000} = 0.6732 \]

### Step 5: Substitute back into the equation
Now we can substitute this back into our equation:
\[ 1683 = MP \times 0.6732 \]

### Step 6: Solve for the marked price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{1683}{0.6732} \]
Calculating this gives:
\[ MP \approx 2500 \]

### Conclusion
Thus, the marked price of the article is Rs. 2,500.

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