Set theory and Venn diagram In a group of 70 cars tested by a garage in Delhi, 15 had faulty tyres, 20 had faulty brakes and 18 exceed the allowable emission limits. Also, 5 cars had faulty tyres and breaks, 6 failed on tyres and emission limits, 10 failed on breaks and emission, and 4 cars were unsatisfactory in all aspects, how many had no fault in these 3 checks?

Easy, we have 70 total subtract 15+20+18=53, giving 17. Then add back the overlaps of any 2 as they got subtracted twice, 6+10+5+17=38. Now deal with the threeway overlap, it got subtracted 3 times (not the 6 I thought, because the overlaps overlap), then added back 3 times. We need to subtract it once more. 38-4=34. 34 cars had no fault when checked,70-34=36 did. Next time show what's been tried, and the problem source.