QUESTION

CSAT

Easy

Maths

Prelims 2015

In a parking area, the total number of wheels of all the cars (four-wheelers) and scooters/motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is:

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Explanation

Let: $x$ = number of two-wheelers (scooters/motorbikes) $y$ = number of four-wheelers (cars)

Given:

Total number of vehicles = $x + y$
Total number of wheels = $2x + 4y$ (since each two-wheeler has 2 wheels and each four-wheeler has 4 wheels)
Total number of wheels = $2(x + y) + 100$

Formulating the equation: $2x + 4y = 2(x + y) + 100$

Simplifying: $2x + 4y = 2x + 2y + 100$ Subtract $2x$ from both sides: $4y = 2y + 100$ Subtract $2y$ from both sides: $2y = 100$ Divide both sides by 2: $y = 50$