# how to draw venn diagrams for difficult questions?Please explain the concept in great detail that i will be able to attempt any difficult question in exam.please illutrate by doing only using a very difficult example.

### Asked by Anishma Joseph | 5th Jul, 2015, 02:50: AM

Expert Answer:

### Let's solve the following problem using venn diagram:
**In a survey of population of 450 people, it is found that 205 can speak English(E), 210 can speak Hindi(H) and 120 people can speak Tamil(T). If 100 people can speak both E and H, 80 can speak both E and T, 35 can speak both H and T, and 20 can speak all the three languages, find the number of people who can speak E but not H or T. Find also the number of people who can speak neither E nor H nor T.**
Solution:
We draw the venn diagram for three categories as follows:
The numbers in the Venn diagram are obtained by simple calculations.
It is given that 20 can speak all three. Hence, we have written 20 in the region common to all three.
Given that 100 can speak both E and H. Hence, 100-20=80 gives the number of people who can speak both E and H but not T.
Similarly, 80 can speak both E and T. Hence, 80-20=60 people can speak both E and T but not H.
Similarly, we get 15 can speak both H and T but not E. All these are shown in the venn diagram.
Also given that total 205 can speak English(E). From the diagram , we already have 80+20+60=160 people in 3 parts of the diagram.
Hence, the number of people who can speak only E but not H or T = 205-160=45.
Also adding all numbers in the three circles we get
45+60+20+80+25+15+95=340.
Hence, people who can speak neither= total number of people - 340 = 450 - 340 = 110.

**In a survey of population of 450 people, it is found that 205 can speak English(E), 210 can speak Hindi(H) and 120 people can speak Tamil(T). If 100 people can speak both E and H, 80 can speak both E and T, 35 can speak both H and T, and 20 can speak all the three languages, find the number of people who can speak E but not H or T. Find also the number of people who can speak neither E nor H nor T.**### Answered by satyajit samal | 7th Jul, 2015, 10:06: AM

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