In a class containing 100 students, 20 know english and 20 do not know Urdu and 10 know neither english nor urdu. The number of students knowing both english and urdu are:
A) 5
B) 15
C) 10
D) 20
Please explain with working.

Question

In a class containing 100 students, 20 know english and 20 do not know Urdu and 10 know neither english nor urdu.  The number of students knowing both english and urdu are:
A) 5
B) 15
C) 10
D) 20
Please explain with working.

ciarán95 · Answer

The best method of solving this is via a Venn diagram. 

Let E = the number of students who know English = 20 (these 20 may know Urdu as well, we are not told)
We will let x = the number of students who know both English and Urdu (we are looking for this).
So, this means the number of students who know English, but do not know Urdu, is 20-x.

We are told that 20 students do not know Urdu. However, we also know that 10 know neither English or Urdu. So, clearly, this means that 10 of these 20 students who do not know Urdu must just know English. Above, we found that this 10 could be written as 20-x. 

So, let 10 = 20 - x and solve for x to find the number of students who know both. I've included the Venn diagram below as it makes it easier to see what's going on as the description can sometimes be confusing.
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