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Q.

The taxi fare in a city is as follows: For the first kilometer, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information.


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a

5x-y+3 = 0

b

5x+y-3 = 0

c

5x+y = 0

d

5x-y-3 = 0 

answer is A.

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Detailed Solution

Given: The distance covered is x km and the total fare is ₹ y. Also, the fate of the first kilometer is ₹ 8 and for the subsequent distance, it is ₹5 per km.
Let the total distance covered = x km
Therefore, subsequent distance = (x - 1) km
The total fare covered = ₹ y
Fare for the 1st kilometer = ₹ 8
Fare per km = ₹ 5
Fare rate for the subsequent distance = 5(x - 1)
The linear equation for the above information is given by,
Total fare = Fare for the first kilometer + Subsequent distance × Fare per km
y = 8 + (x - 1) 5 or, y = 8 + 5x - 5
or, y = 5x + 3
or, 5x - y + 3 = 0
Hence, the correct option is 1.
 
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The taxi fare in a city is as follows: For the first kilometer, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information.