Question

In a survey among students at all the iims, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. The total number of students is 2000.Number of students who like coffee and smoking but not tea is

Answer 1

During the survey it is found that 48% preferred coffee, 54% liked tea and 64% like to smoke.

Now, 28% liked coffee and tea

32% liked to smoke and have tea

30% liked to smoke and have coffee

6% liked none of these.

Now, we can use Venn diagram to solve this problem:

The total percentage should be 100%, so,

$100\%=(48+54+64-28-32-30+x+6)\%$

Where 'x' is the percentage of people who liked all of them.

So,

$100=82+x$

$x=100-82=18$

$x=18\%$

So it is 18% of the total students who like all of them.

Now, we need to find the number of students who like coffee and smoking but not tea.

Refer the diagram:

People who like to smoke and have coffee is:

$30\%-18\%=12\%$

There are 2000 students who were surveyed so 12% of 2000 is:

$12\%\times 2000=0.12\times2000=240$

So, there are 240 students who like to have coffee and smoke but not tea.