Some autorikshaws and bikes are parked in a place. There are 19 in all. The total number of wheels is 45. How many of each vehicle are there?

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Solution

Let the number of auto rickshaws and bikes parked at the place be x and y respectively.

Total number of vehicles = 19

⇒ x + y = 19 … (1)

Number of wheels in a bike = 2

Number of wheels in an auto rickshaw = 3

Total number of wheels = 45

⇒ 3x + 2y = 45 ... (2)

Multiplying equation (1) by 3:

3x + 3y = 57 ... (3)

Subtracting equation (2) from equation (3):

y = 12

Putting the value of y in equation (1):

x + 12 = 19

⇒ x = 19 − 12 = 7

Thus, there were 7 auto rickshaws and 12 bikes parked at the place.

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