In a parking, 2/5 of the vehicles are cycles, 5/12 are cars, 1/6 are scooters and remaining 6 are heavy vehicles. Find the total number of vehicles parked. Also find number of each type of vehicle mentioned above (cycle, car, scooter).
Answers
Step-by-step explanation:
c --> number of cars(4 wheelers) hence 4c no. of wheels
b-->number of bikes(2 wheelers) hence 2b no. of wheels
Total wheels==> 4c + 2b (total number of wheels of all the cars 4 wheelers and bikes 2 wheelers)
Total no. of parked vehicles ==> b+c
Twice no. of parked vehicles==> 2(b+c)
100 more than 2(b+c) ==> 100 + 2(b+c)
FInally
100+2b +2c = 4c +2b
Divide 2 on both sides
==> 50+b+c=2c+b
==>50 + c = 2c (Subtracting b on both sides)
==> 50 = c (Subtracting c on both sides)
So number of cars is 50
Let number of car be x
number of bikes be y
according to question
wheels of all car + wheels of all bike=100 +2(number of total vehicle)
4x + 2y=100 + 2(x+y)
4x=100+2x
2x=100
x=50
number of cars= 50
On substituting the value of x again in equation
we get 2y=2y
This imply that y can be any natural number
total number of cars is 50 and bikes can vary