Question

in a survey of 750 student in school it was found that 520 students like tea ,450 like coffee and 90 didn't like both the drinks? find the number of student who like both the drinks and find a number of a student who don't like tea only ​

Answer 1

Step-by-step explanation:Let me reword the problem by suggesing that 90 people did not like either tea nor coffee. (As written, many more than 90 people did not like both.)

Let’s look at the known groups. 520 people liked tea, some of whom also liked coffee. (We do not yet know how many of these 520 people who liked tea also liked coffee.) We also know that 450 people liked coffee, some of whom also liked tea. (Again, we do not know how many of these 450 people who liked coffee also liked tea.) Clearly, if we add these two groups together, we get 970 people who liked coffee, tea or both. Now, 90 people liked neither. Add these to the mix. We now have 970 people plus 90 people or 1060 people who either drank coffee, tea or both or did not. This is everybody. But we are also told that there were 750 people in all. But some of these 1060 people were included twice. These were those who drink both coffee and tea. The difference between 1060 and 750 is 310. This must represent the number of people who like both coffee and tea. Now, we know that 520 people like tea. Of these, 310 people also like coffee. That leaves 520 - 310 or 210 of the tea drinkers who do not like coffee. Similarly, we know that 450 people like coffee. Of these, 310 also like tea. So, of the 450 coffee drinkers, 450 - 310 or 140 people like coffee only, but not tea. So, we now have the following sets:

TEA:

tea only (and not coffee): 210

tea AND coffee: 310

Of the 520 people who drink tea, 310 like coffee and 210 do not like coffee.

COFFEE:

coffee only (and not tea): 140

coffee AND tea: 310

Of the 450 people who like coffee, 310 like tea and 140 do not.

Again, to answer the question, 210 people like tea only.