The bus fare and train fare of a place from Kolkata were 20 and 30 respectively. Train fare has been increased by 20% and the bus fare has been increased by 10%. The ratio of new train fare to new bus fare is

Options

A. `11:18`
B. `18:11`
C. `5:3`
D. `3:5`

Answer

To solve the problem step by step, we will calculate the new fares for both the bus and the train after their respective increases, and then find the ratio of the new train fare to the new bus fare.

### Step 1: Calculate the new train fare
The original train fare is ₹30. The train fare has been increased by 20%.

- To calculate the increase:
\[ \text{Increase} = \text{Original Fare} \times \frac{\text{Percentage Increase}}{100} = 30 \times \frac{20}{100} = 30 \times 0.2 = 6 \]

- Now, add the increase to the original fare:
\[ \text{New Train Fare} = \text{Original Fare} + \text{Increase} = 30 + 6 = 36 \]

### Step 2: Calculate the new bus fare
The original bus fare is ₹20. The bus fare has been increased by 10%.

- To calculate the increase:
\[ \text{Increase} = \text{Original Fare} \times \frac{\text{Percentage Increase}}{100} = 20 \times \frac{10}{100} = 20 \times 0.1 = 2 \]

- Now, add the increase to the original fare:
\[ \text{New Bus Fare} = \text{Original Fare} + \text{Increase} = 20 + 2 = 22 \]

### Step 3: Find the ratio of the new train fare to the new bus fare
Now that we have the new train fare and the new bus fare, we can find the ratio.

- The new train fare is ₹36 and the new bus fare is ₹22.
- The ratio is given by:
\[ \text{Ratio} = \frac{\text{New Train Fare}}{\text{New Bus Fare}} = \frac{36}{22} \]

- To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD), which is 2:
\[ \frac{36 \div 2}{22 \div 2} = \frac{18}{11} \]

### Final Answer
The ratio of the new train fare to the new bus fare is **18:11**.

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