If the difference between discount of 35% and two successive discounts of 20% on a certain bill is Rs 3, then what is the amount (in Rs) of the bill?

Options

A. 250
B. 300
C. 350
D. 400

Answer

To solve the problem, we need to find the amount of the bill based on the given discounts. Let's break it down step by step.

### Step 1: Understand the Discounts
We have two types of discounts:
1. A single discount of 35%.
2. Two successive discounts of 20%.

### Step 2: Calculate the Effective Discount from Two Successive Discounts
To find the effective discount when applying two successive discounts of 20%, we can use the formula for successive discounts:

\[ \text{Effective Discount} = D_1 + D_2 - \left(\frac{D_1 \times D_2}{100}\right) \]

Where \(D_1\) and \(D_2\) are the two discounts.

Here, both \(D_1\) and \(D_2\) are 20%.

Substituting the values:

\[ \text{Effective Discount} = 20 + 20 - \left(\frac{20 \times 20}{100}\right) \]

Calculating the multiplication:

\[ \frac{20 \times 20}{100} = \frac{400}{100} = 4 \]

Now substituting back:

\[ \text{Effective Discount} = 20 + 20 - 4 = 36\% \]

### Step 3: Set Up the Equation Based on the Given Information
According to the problem, the difference between the discount of 35% and the effective discount of 36% is Rs 3.

So we can write:

\[ 36\% \text{ of Bill} - 35\% \text{ of Bill} = 3 \]

This simplifies to:

\[ (36 - 35)\% \text{ of Bill} = 3 \]

Which implies:

\[ 1\% \text{ of Bill} = 3 \]

### Step 4: Find the Total Amount of the Bill
To find the total amount of the bill, we multiply both sides of the equation by 100:

\[ \text{Bill} = 3 \times 100 = 300 \]

### Conclusion
The amount of the bill is Rs 300.