SOLUTION: In a town 85% of the people speak English, 40% speak kannada and 20% speak Hindi, also {{{matrix(1,2,cross("42%"),"32%")}}} speak English and Kannada, {{{matrix(1,2,cross("23%")

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Question 1039430: In a town 85% of the people speak English, 40% speak kannada
and 20% speak Hindi, also speak English and Kannada,
speak kannada and Hindi. And 10% speak English and Hindi.
Find the percentage of people who can speak all the three languages?
Found 4 solutions by Edwin McCravy, solver91311, ikleyn, AnlytcPhil:
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
Sorry, this has no solution.  One or more of the numbers
you have posted above is incorrect.  Check the source
for which you copied the problem carefully.  You may state 
the corrected problem in the thank-you note form below,
and I'll get back to you by email.  


Edwin
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


I double-checked Edwin's analysis of your problem and he is absolutely correct. Doing the arithmetic with your numbers gives rise to absurdities such as MINUS 21 and 2/3 people out of 100 speak English and Hindi but not Kannada.

John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.
In a town 85% of the people speak English, 40% speak kannada and 20% speak Hindi, also 42% speak English and Kannada,
23% speak kannada and Hindi. And 10% speak English and Hindi. Find the percentage of people who can speak all the three languages?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The input data is wrong.

For example, more people speak English and Kannada (42%) than kannada (40%) - absurd.


Answer by AnlytcPhil(1810)   (Show Source): You can put this solution on YOUR website!

I think I know exactly what the mistakes are! The 42% should
be 32% and the 23% should be 13%.

In a town 85% of the people speak English, 40% speak kannada
and 20% speak Hindi, also speak English and Kannada,
speak kannada and Hindi. And 10% speak English and Hindi.
Find the percentage of people who can speak all the three languages?



Everybody in circle E speaks English.
Everybody in circle K speaks Kannada.
Everybody in circle H speaks Hindi.
If the little letters represent the percentages in
each of the 7 regions, then

p+q+r+s+t+u+v = 100%.  Let's not bother
with the percent marks:

p+q+r+s+t+u+v = 100

In a town 85% of the people speak English,
p+q+s+t = 85

40% speak kannada 
q+r+t+u = 40

and 20% speak Hindi, 
s+t+u+v = 20

also speak English and Kannada,
q+t = 32

speak kannada and Hindi. 
t+u = 13

And 10% speak English and Hindi.
s+t = 10

Find the percentage of people who can speak all the three languages?
So we want the value of t.

The 7 equations in 7 unknowns are

1.   p+q+r+s+t+u+v = 100
2.   p+q+  s+t     =  85
3.     q+r  +t+u   =  40
4.         s+t+u+v =  20
5.     q    +t     =  32
6.           t+u   =  13
7.         s+t     =  10

Let's get all the other 6 letters 
in terms of t:

From 7, 
8.   s = 10-t
From 5,
9.   q = 32-t
From 2,
     p+32-t+10-t+t = 85
     p-t+42 = 85
10.  p = 43+t

From 6,
11.  u = 13-t
8.   s = 10-t
From 4,
     10-t+t+13-t+v = 20
     23-t+v = 20
12.  v = t-3  

9.   q = 32-t
11.  u = 13-t
From 3,
     32-t+r+t+13-t = 40
     r-t+45 = 40
13.  r = t-5

Now that we have all the other 6 letters in terms of t,
we can substitute into 1:

1.   p+q+r+s+t+u+v = 100
     43+t+32-t+t-5+10-t+t+13-t+t-3 = 100
     90+t = 100
     t = 10

That's the answer.  But let's fill in the Venn diagram:
p = 43+t = 43+10 = 53
q = 32-t = 32-10 = 22
r = t-5 = 10-5 = 5
s = 10-t = 10-10 = 0
t = 10
u = 13-t = 3
v = t-3 = 10-3 = 7

So the Venn diagram is:



Edwin
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