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
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.