Question

From Bangalore bus stand, if we buy 2 tickets to Malleshwaram and 3 tickets to Yeshwanthpur, the total cost is ₹46; but if we buy 3 tickets to Malleshwaram and 5 tickets to Yeshwanthpur, then the total cost is ₹74. Find the fares from Bangalore bus stand to Malleshwaram and to Yeshwanthpur respectively.

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

Answer 1

The correct option is C ₹8 and ₹10

Let the fare from Bangalore bus stand to Malleshwaram be ₹x
and the fare from Bangalore bus stand to Yeshwanthpur be ₹y.
According to the given situations, 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
Adding the two equations, we get,
$-y=-10$
$\Rightarrow y=10$

$Substitutey=10inequation\left(i\right)$
$2x+3\left(10\right)=46$
$2x+30=46$
$2x=46-30$
$2x=16$
$x=8$
Hence fares from Bangalore bus stand to Malleshwaram and Yeswanthpur are ₹8 and ₹10 respectively.