The MP of a shirt is Rs524 7. Two successive discounts offered by the shopkeeper on the shirt is 18.18% and 22.22%. Find the total discount .

Options

A. 1943.5
B. 1431
C. 1888
D. 1908

Answer

To solve the problem of finding the total discount on a shirt with a market price of Rs 5247 and two successive discounts of 18.18% and 22.22%, we can follow these steps:

### Step 1: Identify the Discounts
The two successive discounts are:
- Discount A = 18.18%
- Discount B = 22.22%

### Step 2: Use the Successive Discount Formula
The formula for calculating the total discount when two successive discounts are applied is:
\[ \text{Total Discount} = A + B - \frac{A \times B}{100} \]
Substituting the values of A and B:
\[ \text{Total Discount} = 18.18 + 22.22 - \frac{18.18 \times 22.22}{100} \]

### Step 3: Calculate the Product of Discounts
First, calculate the product of A and B:
\[ 18.18 \times 22.22 = 403.95 \]

### Step 4: Substitute and Simplify
Now, substitute this value back into the total discount formula:
\[ \text{Total Discount} = 18.18 + 22.22 - \frac{403.95}{100} \]
\[ \text{Total Discount} = 18.18 + 22.22 - 4.0395 \]
\[ \text{Total Discount} = 40.4 - 4.0395 \approx 36.36 \]

### Step 5: Round the Total Discount
Rounding off to two decimal places, we find:
\[ \text{Total Discount} \approx 36.36\% \]

### Step 6: Calculate the Discount Amount
To find the discount amount in rupees, we apply the total discount percentage to the market price:
\[ \text{Discount Amount} = \frac{36.36}{100} \times 5247 \]
Calculating this gives:
\[ \text{Discount Amount} = 0.3636 \times 5247 \approx 1908.36 \]

### Step 7: Round the Discount Amount
Rounding the discount amount to the nearest whole number:
\[ \text{Discount Amount} \approx Rs 1908 \]

### Final Answer
The total discount amount on the shirt is approximately Rs 1908.

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