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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
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B
₹12 and ₹10
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C
₹10 and ₹12
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D
₹8 and ₹10
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Solution

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 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
y=10

Substitute y=10 in equation (i)
2x+3(10)=46
2x+30=46
2x=4630
2x=16
x=8
Hence fares from Bangalore bus stand to Malleshwaram and Yeswanthpur are ₹8 and ₹10 respectively.

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