Today's Puzzle - What percentage of houses do not have tubelight, bulb and fan?

Thursday, February 24, 2011

Question:

There is a shortage of tubelights, bulbs and fans in a village - Kharghar. It is

found that

• All houses do not have either tubelight or bulb or fan.

• exactly 19% of houses do not have just one of these.

• atleast 67% of houses do not have tubelights.

• atleast 83% of houses do not have bulbs.

• atleast 73% of houses do not have fans.

What percentage of houses do not have tubelight, bulb and fan?

Answer

42% houses do not have tubelight, bulb and fan.

Let's assume that there are 100 houses. Hence, there should be total 300 items

i.e. 100 tubelights, 100 bulbs and 100 fans.

From the given data, we know that there is shortage of atleast (67+83+73) 223

items in every 100 houses.

Also, exactly 19 houses do not have just one item. It means that remaining 81

houses should account for the shortage of remaining (223-19) 204 items. If those

remaining 81 houses do not have 2 items each, there would be a shortage of 162

items. But total of 204 items are short. Hence, atleast (204-162) 42 houses do

not have all 3 items - tubelight, bulb and fan.

Thus, 42% houses do not have tubelight, bulb and fan.