# What percentage of cars do not have steering wheel, horn and headlight?

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In a car manufacturing plant at Detroit, there is a shortage of steering wheels, horns and headlights during manufacturing of a particular batch of cars. It is found that:
All cars do not have either steering wheel or horn or headlight
Exactly 19% of cars do not have just one of these
Atleast 67% of cars do not have steering wheels
Atleast 83% of cars do not have horns
Atleast 73% of cars do not have headlights
What percentage of cars do not have steering wheel, horn and headlight?

posted Sep 15, 2015

42% cars do not have steering wheel, horn and headlight.

Since figures are supplied in percentages, let us assume that there are 100 cars. Hence, there should be total 300 items i.e. 100 steering wheels, 100 horns and 100 headlights.

From the given data, we know that there is shortage of at least (67+83+73) 223 items in every 100 cars.

Also, exactly 19 cars do not have just one item. It means that remaining 81 cars should account for the shortage of remaining (223-19) 204 items.

If those remaining 81 cars do not have 2 items each, there would be a shortage of 162 items. But total of 204 items are short.

Hence, at least (204-162) 42 cars do not have all 3 items - steering wheel, horn and headlight.