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

Options

A. Rs. 200
B. Rs. 220
C. Rs. 1,100
D. Rs. 2,200

Answer

To solve the problem step by step, we need to find the amount of the bill based on the given discounts.

### Step 1: Define the variables
Let the original amount of the bill be \( X \).

### Step 2: Calculate the amount after a 35% discount
When a discount of 35% is applied, the amount paid will be:
\[ \text{Amount after 35% discount} = X - 0.35X = 0.65X \]

### Step 3: Calculate the amount after two successive 20% discounts
When two successive discounts of 20% are applied, we first calculate the amount after the first 20% discount:
\[ \text{Amount after first 20% discount} = X - 0.20X = 0.80X \]
Now, applying a second 20% discount on the new amount:
\[ \text{Amount after second 20% discount} = 0.80X - 0.20(0.80X) = 0.80X - 0.16X = 0.64X \]

### Step 4: Set up the equation based on the difference
According to the problem, the difference between the amount after a 35% discount and the amount after two successive 20% discounts is Rs. 22:
\[ 0.65X - 0.64X = 22 \]

### Step 5: Simplify the equation
This simplifies to:
\[ 0.01X = 22 \]

### Step 6: Solve for \( X \)
To find \( X \), 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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