Question

The total cost of 2 tickets to station A and 3 tickets to station B is ₹ 46. Also, the total cost of 3 tickets to station A and 5 tickets to station B₹ 74. Find the fares to station A and to station B.

• A. ₹ 10 and ₹ 8
• B. ₹ 12 and ₹ 10
• C. ₹ 10 and ₹ 12
• D. ₹ 8 and ₹ 10

Answer 1

The correct option is D

₹ 8 and ₹ 10

Let the fare to station A be ₹ x and the fare to station B be ₹ y
According to the given conditions, we have
2x + 3y = 46 .....(i)
3x + 5y = 74 .....(ii)
Multiplying equation (i) by 3 and equation (ii) by -2 we get,
6x + 9y = 138
-6x -10y = -148
____________
$\Rightarrow -y=-10$
$\Rightarrow y=10$
$Substitutey=10inequation\left(i\right)$
$2x+3\left(10\right)=46$
$2x+30=46$
$2x=46-30$
$2x=16$
$x=8$
Hence fares to Station A and to Station B are ₹ 8 and ₹ 10 respectively.