venn diagram.100 people present.75 speak hindi.40 speak english.how many speak both?

## in a group of 100 people threr are 75 people who can speak hindi and 40 who speak english.how many can speak both?

# 4 Answers

Hello Abinaya.

This is simpler than it looks...

The key information here is that there are 100 people in total!

Okay, so there are 75 people who speak Hindi and then 40 who speak English. I know that by adding them I get a total of 115 people!

Wait... that's 15 more than 100 people that you were told in the beginning...

Where did the 15 extra come from?!

They must have been counted TWICE - once for the "people speaking Hindi" group and then again for the "people speaking English" group.

So... it looks more like this

Hindi ONLY - 60 people

English & Hindi BOTH - 15 people

English ONLY - 25 people

So if you look at this and ask the simple questions, how many speak English you get 15 + 25 = 40. By the same logic if you ask how many speak Hindi you get 60 + 15 = 75.

Hope it helped!

Best,

Tae

Technically there is not enough information to answer the question, not unless we assume that every person speaks either hindi, english or both. It's entirely possible that 40 people all speak both hindi and english, 35 people speak hindi only and the remaining 25 speak some other language.

But let's assume that's not the case.

My advice when creating a venn diagram is to always start in the middle and work your way out.

So then, you know that you have 2 bubbles with some overlap.

in the first bubble there should be 40 and in the second bubble there should be 75 and combined there should be 100.

but we have a total of 40 + 75 = 115 people who speak either english or hindi, which means that we double counted 115 - 100 = 15 times.

Because. since there are only two bubbles, there is no other way we could have gotten more than 100 total.

If we had three bubbles, then it would be a bit more complicated, because we would have to figure out whether we double or triple counted those extra 15.

But in this case we found that the middle number of the venn diagram should be 15. So, then we start to work our way out.

Now for the English bubble, we know that we should have a total of 40 people, but we already know that there was an overlap of 15 people.

Then, there are two ways that we can solve this:

1.) 40 people speak English, and 15 people speak both, so the total number of people who speak only English must be 40 - 15 = 25.

OR

2.) We have a total of 100 people, and 75 people speak either hindi or both. So, the number of people who speak only english should be the same as the number of people who do not speak hindi, ie. 100 - 75 = 25.

And now that we know how many people speak only english and how many people speak both, there are 3 ways to find how many people speak only hindi (which should be the last remaining bubble to fill in).

1.) we know that the total number of people who speak hindi is 75, and the total number that speak both is 15. So, we take the difference, 75 - 15 = 60 people.

OR

2.) We know that the total number of people questioned was 100. And the number of people who speak English was 40. So, we take the difference 100 - 40 = 60 people who speak only hindi, or people who do not speak english. In this case those two things are one in the same.

OR

3.) We know that the total number of people questioned was 100. And we have one unfilled bubble left. So we start with 100, and subtract what's already filled in to the other bubbles, which should give us 100 - 15 - 25 = 60 people.

If each one speak only one of the two languages, then the total number of people is 115, which means that 15 people speak both languages.

75+40 - 100 = 15 people <==Answer

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Attn: Drawing a Venn diagram can help you. From the Venn diagram, you can get

A∪B = A+B-A∩B

So, A∩B = A+B - A∪B

Total of 75 and 40 = 115.

Total number of people= 100

So, the 'extras' = 15 people.

Now, these can speak both.

Simple.