The difference between a discount of `35%` and two successive discounts of `20%` on a certain bill was Rs. 22 Find the amount of the bill.

Options

A. Rs. 1100
B. Rs. 2000
C. Rs. 2200
D. Rs. 1000

Answer

To solve the problem step by step, we will follow this approach:

### 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 Amount after Two Successive Discounts of 20%
Let the original bill amount be \( x \).

After the first 20% discount:
- Amount after first discount = \( x \times (1 - 0.20) = x \times 0.80 \)

After the second 20% discount on the new amount:
- Amount after second discount = \( (x \times 0.80) \times (1 - 0.20) = (x \times 0.80) \times 0.80 = x \times 0.64 \)

### Step 3: Calculate the Amount after a 35% Discount
Now, let's calculate the amount after a 35% discount:
- Amount after 35% discount = \( x \times (1 - 0.35) = x \times 0.65 \)

### Step 4: Set Up the Equation Based on the Given Difference
According to the problem, the difference between the two amounts is Rs. 22:
\[ x \times 0.65 - x \times 0.64 = 22 \]

### Step 5: Simplify the Equation
Factor out \( x \):
\[ x \times (0.65 - 0.64) = 22 \]
\[ x \times 0.01 = 22 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 0.01:
\[ x = \frac{22}{0.01} = 2200 \]

### Conclusion
The amount of the bill is Rs. 2200.

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