Solving Train Ticket Fare Ratio Problem

Let's break down the problem step-by-step to find the ratio of the new train ticket fares.

Understanding the Initial Train Ticket Fares

We are given the initial train ticket fares for two classes:

• 2nd class AC fare from A to B: Rs. 2,500
• 3rd class AC fare from A to B: Rs. 2,000

Calculating the New 2nd Class AC Fare

The fare for 2nd class AC is increased by 20%. To find the new fare, we first calculate the increase amount and then add it to the original fare.

• Original 2nd class AC fare = Rs. 2,500
• Percentage increase = 20%

Increase amount = 20% of Rs. 2,500

This can be calculated as:

$$ \text{Increase} = \frac{20}{100} \times 2500 $$

$$ \text{Increase} = 0.20 \times 2500 $$

$$ \text{Increase} = 500 $$

So, the increase in the 2nd class AC fare is Rs. 500.

New 2nd class AC fare = Original fare + Increase amount

$$ \text{New Fare (2nd AC)} = 2500 + 500 = 3000 $$

The new 2nd class AC fare is Rs. 3,000.

Calculating the New 3rd Class AC Fare

The fare for 3rd class AC is increased by 10%. We follow a similar process to find the new fare.

• Original 3rd class AC fare = Rs. 2,000
• Percentage increase = 10%

Increase amount = 10% of Rs. 2,000

This can be calculated as:

$$ \text{Increase} = \frac{10}{100} \times 2000 $$

$$ \text{Increase} = 0.10 \times 2000 $$

$$ \text{Increase} = 200 $$

So, the increase in the 3rd class AC fare is Rs. 200.

New 3rd class AC fare = Original fare + Increase amount

$$ \text{New Fare (3rd AC)} = 2000 + 200 = 2200 $$

The new 3rd class AC fare is Rs. 2,200.

Finding the Ratio of New Fares

Now we need to find the ratio of the new fares of 2nd class AC and 3rd class AC.

Ratio = New 2nd class AC fare : New 3rd class AC fare

Ratio = Rs. 3,000 : Rs. 2,200

To simplify the ratio, we can divide both numbers by their greatest common divisor. We can start by dividing by 100.

$$ \frac{3000}{100} : \frac{2200}{100} $$

$$ 30 : 22 $$

Both 30 and 22 are divisible by 2.

$$ \frac{30}{2} : \frac{22}{2} $$

$$ 15 : 11 $$

The ratio 15 : 11 is in its simplest form because 15 and 11 have no common factors other than 1.

Final Answer Summary

Initial 2nd class AC fare: Rs. 2,500

New 2nd class AC fare (after 20% increase): Rs. 3,000

Initial 3rd class AC fare: Rs. 2,000

New 3rd class AC fare (after 10% increase): Rs. 2,200

Ratio of new fares (2nd AC : 3rd AC): 15 : 11

The ratio of the new fares of 2nd class AC and 3rd class AC is 15 : 11.

Revision Table: Train Fare Calculation

Additional Information: Percentage and Ratio Concepts

Percentage: A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". For example, 20% means 20 out of 100, or $\frac{20}{100}$. Calculating a percentage increase involves finding what that percentage of the original amount is, and then adding it to the original amount.

Ratio: A ratio is a way to compare two or more quantities. It shows the relationship between the quantities. Ratios can be written with a colon (e.g., 3:4), as a fraction (e.g., $\frac{3}{4}$), or using the word "to" (e.g., 3 to 4). Ratios should usually be simplified to their lowest terms by dividing all parts of the ratio by their greatest common divisor.

In this train ticket fare problem, we first used percentage concepts to find the new fares after the increase. Then, we used ratio concepts to compare these two new fare amounts and express their relationship in a simple form.