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
