# set Theory

• Jan 3rd 2009, 04:25 AM
pmmeeran
set Theory
In a survey of 1000 customers, the number of people who used various types of tea leaves were found to be as follows.

A type only 150, A and C type 90

A type but not B 210, C type 360

A type 240, B and C type 100

None 340

Find

(i) How many buy "C" type only

(ii) How many buy A and B types

(iii) Number of people buying B and C type but not A type ?

(iV) How many buy "B" type only ?

Please solve the problem and show the steps

thanks
• Jan 3rd 2009, 07:00 PM
Jhevon
Quote:

Originally Posted by pmmeeran
In a survey of 1000 customers, the number of people who used various types of tea leaves were found to be as follows.

A type only 150, A and C type 90

A type but not B 210, C type 360

A type 240, B and C type 100

None 340

Find

(i) How many buy "C" type only

(ii) How many buy A and B types

(iii) Number of people buying B and C type but not A type ?

(iV) How many buy "B" type only ?

Please solve the problem and show the steps

thanks

start by drawing a Venn diagram. see below.

fill in the numbers as the problem directs. can you do that?

if you can do that, can you then answer the questions?
• Jan 19th 2009, 09:25 PM
sumit2009
Quote:

Originally Posted by pmmeeran
In a survey of 1000 customers, the number of people who used various types of tea leaves were found to be as follows.

A type only 150, A and C type 90

A type but not B 210, C type 360

A type 240, B and C type 100

None 340

Find

(i) How many buy "C" type only

(ii) How many buy A and B types

(iii) Number of people buying B and C type but not A type ?

(iV) How many buy "B" type only ?

Please solve the problem and show the steps

thanks

see the attached Venn dig.
from the given condition we have following 7 equations

a=150
f+g=90
a+f=210
d+e+f+g=360
a+b+f+g=240
g+d=100
a+b+c+d+e+f+g=1000-340

now there are 7 unknowns and 7 equations
solve them to find the value of a,b,c,d,e,f,g

answer for 1) buy "C" type only=e
2)A and B types=b+g
3) B and C type but not A type=d
4)B" type only=c
• Jan 20th 2009, 11:14 PM
princess_21
Quote:

Originally Posted by sumit2009
see the attached Venn dig.
from the given condition we have following 7 equations

a=150
f+g=90
a+f=210
d+e+f+g=360
a+b+f+g=240
g+d=100
a+b+c+d+e+f+g=1000-340

now there are 7 unknowns and 7 equations
solve them to find the value of a,b,c,d,e,f,g

answer for 1) buy "C" type only=e
2)A and B types=b+g
3) B and C type but not A type=d
4)B" type only=c

try doing this..
A type only=a=150
A and C type= f+g=90
A but not B=a+f=210
C type =d+e+f+g=360
A =a+b+f+g=240
B and C=g+d=100
none=h=340

then we have the value of a=150, try subtracting a from "A but not B" that is a+f=210....
f=210-150
f=60

then in the A and C type, that is f+g=90, subtract f to get g..
f+g=90
g=90-60
g=30

then in the A type, a+b+f+g=240, subtract a, f and g to get b..
a+b+f+g=240
b=240-150-30-60
b=0

then in the B and C type, g+d=100, subtract g to get d..
g+d=100
d=100-30
d=70

then in the C type.. d+e+f+g=360, subtract d, f and g from 360 to get e..
d+e+f+g=360
e=360 -70- 60-30
e=360-150
e=200

none=h=340

then we have:
a=150
b=0
c=?
d=70
e=200
f=60
g=30
h=340

add the following and subtract from 1000.
1000=a+b+c+d+e+f+g+h
c=1000-850
c=150

answer for 1) buy "C" type only=e = 200
2)A and B types=b+g =30
3) B and C type but not A type=d =70
4)B" type only=c =150

i think that's all.
• Jan 25th 2009, 07:10 AM
pmmeeran
Thank you very much Princes 21 and Sumit 2009(Evilgrin)
• Jan 25th 2009, 07:25 AM
skeeter
Quote:

Originally Posted by pmmeeran
Thank you very much Princes 21 and Sumit 2009(Evilgrin)

no thanks for Jhevon?
• Jan 25th 2009, 07:33 AM
pmmeeran
Thanks for all(Bow)