In a road worthiness test on 240 cars, 60% passed. The number that failed had faults in Clutch, Brakes and Steering as follows: Clutch only – 28, Clutch and Steering – 14; Clutch, Steering and Brakes – 8; Clutch and Brakes – 20; Brakes and Steering only – 6. The number of cars with faults in Steering only is twice the number of cars with faults in Brakes only.
(a) Draw a Venn Diagram to illustrate this information.
(b) How many cars had : (i) Faulty Brakes? (ii) Only one fault?
Explanation
(a)
(b) From the Venn Diagram above,
28 + 2x + x + 12 + 6 + 6 + 8 = 96
60 + 3x = 96
3x = 36
x = 12
(i) Faulty brakes = 12 + 12 + 8 + 6 =38
(ii) Cars with only one fault = 28 + 2x + x
= 28 + 3x = 28 + 3(12)
= 28 + 36 = 64