Question

In a car park there are 125 cars 3p motorbikes 2q lorries and 20 buses one of the vehicles leves the car park at random give that the probability that the vehile is a motorbike is 3/40 are probability that the vehile is a bus is 1/10 from a pair of linear equations in p and q​

Answer 1

$\sf\small\underline\red{Given:-}$

In a car park 125 cars , 3p motorbikes , 2q lorries and 20 buses. One of vehicle leave the park at random . probability that the vehicle is a motorbike = 3/40 & bus = 1/10

$\sf\small\underline\red{Find:-}$

The values of p and q.

$\sf\small\underline\red{Solution:-}$

Cars - 125

Motorbikes - 3p

lorries - 2q

Buses - 20

Total = 125 + 3p + 2q + 20

= 145 + 3p + 2q

Probability of motorbike = 3p/( 145 + 3p + 2q) = 3/40

=> 40 p = 145 + 3p + 2q

=> 37p - 145 = 2q

=> 37p - 2q = 145

Probability of bus = 20/( 145 + 3p + 2q) = 1/10

=> 200 = 145 + 3p + 2q

=> 55 - 3p = 2q

=> 3p + 2q = 55

Adding both

40p = 200

=> p = 5

=> 3 * 5 + 2q = 55

=>2q = 40

=> q = 20

37p - 2q = 145 ,

3p + 2q = 55

p = 5 , q = 20

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