Question

If we buy 2 tickets from station A to station B and 3 from station A to C, we have to pay Rs. 795. But 3 tickets from station A to B and 5 tickets from station A to C cost a total of Rs. 1,300. What is the fare from station A to C?

• A. Rs. 200
• B. Rs. 75
• C. Rs. 215
• D. Rs. 180

Hint:

For fare problems, always set up equations using the given conditions and solve using elimination or substitution.

Answer 1

The Correct Option is C

Step 1: Define variables
Let: - The fare from station A to B be \( x \). - The fare from station A to C be \( y \).
Step 2: Formulate equations
From the given information: \[ 2x + 3y = 795 \] \[ 3x + 5y = 1300 \] Step 3: Solve for \( x \) and \( y \)
Multiply the first equation by 3 and the second equation by 2 to align the coefficients of \( x \): \[ 6x + 9y = 2385 \] \[ 6x + 10y = 2600 \] Subtracting both equations: \[ (6x + 10y) - (6x + 9y) = 2600 - 2385 \] \[ y = 215 \] Substituting \( y = 215 \) in \( 2x + 3(215) = 795 \): \[ 2x + 645 = 795 \] \[ 2x = 150 \] \[ x = 75 \] Thus, the correct answer is Rs. 215.