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. ₹ 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 from Bangalore bus stand to Malleshwaram be ₹ x
and the fare from Bangalore bus stand to Yeshwanthpur be ₹ y.
According to the given conditions, 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 ₹ 8 and ₹ 10 respectively.