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...
Question 1 Report
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?
Answer Details
(a) Venn diagram
Let the three sets be:
- C = cars with faulty clutch
- B = cars with faulty brakes
- S = cars with faulty steering
(b) Calculation
Number that passed:
\[60\%\text{ of }240=\frac{60}{100}\times240=144\]
Therefore, number that failed:
\[240-144=96\]
The given numbers for the two-set intersections include the cars with all three faults. Hence:
\[C\cap S\text{ only}=14-8=6\]
\[C\cap B\text{ only}=20-8=12\]
Let the number with brakes only be \(x\). Then the number with steering only is \(2x\).
From the Venn diagram:
\[28+6+8+12+6+x+2x=96\]
\[60+3x=96\]
\[3x=36\]
\[x=12\]
Thus, brakes only \(=12\), while steering only \(=2(12)=24\).
(i) Cars with faulty brakes
\[12+12+6+8=38\]
\[\boxed{38\text{ cars}}\]
(ii) Cars with only one fault
\[28+12+24=64\]
\[\boxed{64\text{ cars}}\]
Download The App On Google Playstore
Everything you need to excel in your exams
