Out of 2000 employees in a office 48 % preferred cofee, 54% liked tea , 64% used to smoke - Maths - Sets

Question

Out of 2000 employees in a office 48 % preferred cofee, 54%
liked tea , 64% used to smoke Out of th etotal employee 28% used
cofee and tea , 32% used tea and smoke and 30% prefered cofee and
smoke and only 6% did none of these The number having all th
ethrree is ?

Harleen Birdi · Accepted Answer

Let us define the following sets
C: People like to have coffee
T: People like to have tea
S: People like to have smoke
Total employees = 2000
So,
n(C) = 48% of 2000 = 960
n(T) = 54% of 2000 = 1080
n(S) = 64% of 2000 = 1280
n(C âˆ© T) = 28% of 2000 = 560
n(T âˆ© S) = 32% of 2000 = 640
n(C âˆ© S) = 30% of 2000 = 600
n(C âˆ© S âˆª T) = 6%
of 2000 = 120
â‡’ n(C âˆª S
âˆª T) = 2000 â€“ 120 = 1880
Using the formula,
n(C âˆª S âˆª T) =
n(C) + n(S) + n(T) â€“
n(C âˆ© S) â€“
n(S âˆ© T) â€“
n(C âˆ© T) + n(C
âˆ© S âˆ© T)
â‡’ 1880 = 960 + 1280 + 1080 - 600
â€“ 640 â€“ 560 + n(C
âˆ© S âˆ© T)
â‡’ n(C âˆ© S
âˆ© T) = 360
Hence, number of people having all three is 360

Out of 2000 employees in a office 48 % preferred cofee, 54% liked tea , 64% used to smoke . Out of th etotal employee 28% used cofee and tea , 32% used tea and smoke and 30% prefered cofee and smoke and only 6% did none of these . The number having all th ethrree is ?