The marked price of an article is Rs 4800. If three successive discounts, each of k%, on the marked price is equal to a single discount of Rs 3481.80. What will be the discount (in Rs), if only two discounts of k% each were given on the marked price?

Options

A. Rs 2277
B. Rs 2772
C. Rs 2727
D. Rs 2722

Answer

To solve the problem step by step, we need to find the discount amount when two successive discounts of k% are applied to a marked price of Rs 4800. The process involves the following steps:

### Step 1: Understand the problem
We know the marked price (MP) of the article is Rs 4800. We are given that three successive discounts of k% each result in a single discount of Rs 3481.80.

### Step 2: Calculate the selling price after three discounts
The selling price (SP) after three successive discounts can be calculated using the formula:
\[ SP = MP \times \left(1 - \frac{k}{100}\right)^3 \]

Given that the SP is equal to the marked price minus the total discount:
\[ SP = MP - \text{Total Discount} \]
Where Total Discount = MP - SP = 4800 - 3481.80 = 1318.20

### Step 3: Set up the equation
From the above, we can set up the equation:
\[ 3481.80 = 4800 \times \left(1 - \frac{k}{100}\right)^3 \]

### Step 4: Simplify the equation
Dividing both sides by 4800:
\[ \frac{3481.80}{4800} = \left(1 - \frac{k}{100}\right)^3 \]
Calculating the left side:
\[ \frac{3481.80}{4800} = 0.725375 \]

### Step 5: Take the cube root
Now, we take the cube root of both sides to find \( 1 - \frac{k}{100} \):
\[ 1 - \frac{k}{100} = \sqrt[3]{0.725375} \]
Calculating the cube root gives:
\[ 1 - \frac{k}{100} \approx 0.895 \]

### Step 6: Solve for k
Now, we can solve for k:
\[ \frac{k}{100} = 1 - 0.895 \]
\[ \frac{k}{100} = 0.105 \]
\[ k = 10.5 \]

### Step 7: Calculate the discount for two discounts of k%
Now we need to calculate the discount when only two discounts of k% are applied:
\[ SP = MP \times \left(1 - \frac{k}{100}\right)^2 \]
Substituting k = 10.5:
\[ SP = 4800 \times \left(1 - 0.105\right)^2 \]
\[ SP = 4800 \times (0.895)^2 \]
Calculating \( (0.895)^2 \):
\[ (0.895)^2 \approx 0.801025 \]
So,
\[ SP \approx 4800 \times 0.801025 \approx 3844.92 \]

### Step 8: Calculate the discount amount
The discount amount when two discounts are applied is:
\[ \text{Discount} = MP - SP \]
\[ \text{Discount} = 4800 - 3844.92 \approx 955.08 \]

### Final Answer
The discount amount when two discounts of k% are applied is approximately Rs 955.08.

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