A 20% hike in bus fare resulted in a 10% fall in passenger traffic, still the daily collection at the bus depot increased by Rs 150. The daily collection at the depot after the fare hike is

Options

A. 1600
B. 1750
C. 2025
D. 1875

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Define the Variables
Let the original bus fare per person be Rs. X.

### Step 2: Calculate the New Fare After the Hike
A 20% hike in the bus fare means the new fare will be:
\[ \text{New Fare} = X + 0.20X = 1.20X \]

### Step 3: Determine the Impact on Passenger Traffic
A 10% fall in passenger traffic means that if the original number of passengers is P, the new number of passengers will be:
\[ \text{New Passengers} = P - 0.10P = 0.90P \]

### Step 4: Calculate the Original Daily Collection
The original daily collection at the bus depot can be calculated as:
\[ \text{Original Collection} = \text{Original Fare} \times \text{Original Passengers} = X \times P = XP \]

### Step 5: Calculate the New Daily Collection After the Fare Hike
The new daily collection after the fare hike will be:
\[ \text{New Collection} = \text{New Fare} \times \text{New Passengers} = (1.20X) \times (0.90P) = 1.08XP \]

### Step 6: Set Up the Equation for the Increase in Collection
According to the problem, the new collection is Rs. 150 more than the original collection:
\[ 1.08XP = XP + 150 \]

### Step 7: Simplify the Equation
Subtract XP from both sides:
\[ 1.08XP - XP = 150 \]
\[ 0.08XP = 150 \]

### Step 8: Solve for XP
Now, divide both sides by 0.08 to find XP:
\[ XP = \frac{150}{0.08} = 1875 \]

### Step 9: Calculate the New Daily Collection
Now that we have the original collection (XP), we can find the new collection:
\[ \text{New Collection} = XP + 150 = 1875 + 150 = 2025 \]

### Final Answer
The daily collection at the depot after the fare hike is Rs. 2025.

---