In a group of 70 cars tested by a garage in Delhi, 15 had faulty tyres, 20 had faulty brakes, 18 exceed the allowable emission limits. Also, 5 cars had faulty tyres and braked, 6 failed on tyres and emission, 10 failed on brakes and emission, and 4 cars were unsatisfactory in the three respects. How many cars had no faults in these three checks? Draw and appropriate Venn diagram.
Answers
Given : In a group of 70 cars tested by a garage in Delhi, 15 had faulty tyres, 20 had faulty brakes, 18 exceed the allowable emission limits. Also, 5 cars had faulty tyres and braked, 6 failed on tyres and emission, 10 failed on brakes and emission, and 4 cars were unsatisfactory in the three respects.
To Find : How many cars had no faults in these three checks
Solution:
Total Cars C = 70
Faulty Tyres T = 15
Faulty brakes B = 20
Emission Limit E = 18
Faulty Tyres & Brakes T ∩ B = 5
Failed on tyres and emission = T ∩ E = 6
Failed on brakes and emission = B ∩ E = 10
Failed in all T ∩ B ∩ E = 4
No Fault = N
C = T + B + E - T ∩ B - T ∩ E - B ∩ E + T ∩ B ∩ E + N
=> 70 = 15 + 20 + 18 - 5 - 6 - 10 + 4 + N
=> N = 34
34 Cars have no fault
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