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
(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
see the attached Venn dig.
from the given condition we have following 7 equations
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
B and C=g+d=100
then we have the value of a=150, try subtracting a from "A but not B" that is a+f=210....
then in the A and C type, that is f+g=90, subtract f to get g..
then in the A type, a+b+f+g=240, subtract a, f and g to get b..
then in the B and C type, g+d=100, subtract g to get d..
then in the C type.. d+e+f+g=360, subtract d, f and g from 360 to get e..
e=360 -70- 60-30
then we have:
add the following and subtract from 1000.
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.