Inclusive of an 18% peak-time surcharge a taxi fare came to Rs.531. What would the payable amount have been without the surcharge?

Options

A. Rs.440
B. Rs.425
C. Rs.450
D. Rs.475

Answer

To find the taxi fare without the 18% peak-time surcharge, we can follow these steps:

### Step 1: Define the variables
Let the taxi fare without the surcharge be Rs. X.

### Step 2: Understand the surcharge
The total fare, which includes the surcharge, is given as Rs. 531. The surcharge is 18% of the fare without the surcharge. Therefore, the total fare can be expressed as:
\[ \text{Total Fare} = \text{Fare without surcharge} + \text{Surcharge} \]
This can be written as:
\[ 531 = X + 0.18X \]

### Step 3: Combine the terms
Combine the terms on the right side:
\[ 531 = X + 0.18X \]
This simplifies to:
\[ 531 = 1.18X \]

### Step 4: Solve for X
To find the value of X, we rearrange the equation:
\[ X = \frac{531}{1.18} \]

### Step 5: Calculate the value
Now, we perform the division:
\[ X = \frac{531 \times 100}{118} \]
Calculating this gives:
\[ X = 450 \]

### Conclusion
The payable amount without the surcharge is Rs. 450.

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