Question

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

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

Answer 1

The correct option is D

Rs. 8 and Rs. 10

Let the fare from Bangalore bus stand to Malleshwaram be Rs x
and the fare from Bangalore bus stand to Yeshwanthpur be Rs y.
According to the given situations, we have
2x + 3y = 46 .....(i)
3x + 5y = 74 .....(ii)
Multiply 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 from Bangalore bus stand to Malleshwaram and Yeswanthpur are Rs. 8 and Rs. 10 respectively.