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Brindavan Express leave Chennai Central ...

Brindavan Express leave Chennai Central Station every day at `07.50` am and goes to Bangalore City Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio `1 : 4`. The fare for this travel is in the ratio `3 :1`. The total fare collected was Rs. `224000`/- ( Rs. Two lakhs twenty four thousand only)- What was the fare collected from I class passengers on that day?

A

Rs. 32000

B

Rs. 96000

C

Rs. 128000

D

Rs.5,00,000

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will follow these steps: ### Step 1: Define the variables for passengers Let the number of I class passengers be \( x \). Since the ratio of I class to II class passengers is \( 1:4 \), the number of II class passengers will be \( 4x \). ### Step 2: Define the fare for each class Let the fare for I class be \( 3y \) and the fare for II class be \( y \). The ratio of the fares is given as \( 3:1 \). ### Step 3: Calculate the total fare collected from each class The total fare collected from I class passengers can be calculated as: \[ \text{Fare from I class} = \text{Number of I class passengers} \times \text{Fare for I class} = x \times 3y = 3xy \] The total fare collected from II class passengers can be calculated as: \[ \text{Fare from II class} = \text{Number of II class passengers} \times \text{Fare for II class} = 4x \times y = 4xy \] ### Step 4: Calculate the total fare collected The total fare collected from both classes is: \[ \text{Total fare} = \text{Fare from I class} + \text{Fare from II class} = 3xy + 4xy = 7xy \] We know from the problem that the total fare collected is Rs. 224,000: \[ 7xy = 224000 \] ### Step 5: Solve for \( xy \) To find \( xy \), we divide both sides by 7: \[ xy = \frac{224000}{7} = 32000 \] ### Step 6: Calculate the fare collected from I class passengers Now, we can find the fare collected from I class passengers: \[ \text{Fare from I class} = 3xy = 3 \times 32000 = 96000 \] ### Final Answer The fare collected from I class passengers on that day is Rs. 96,000. ---
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