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Out of 2000 employees in an office 48% preferred Coffee (c), 54% liked (T), 64% used to smoke (S). Out of the total 28% used C and T, 32% used T and S and 30% preferred C and S, only 6% did none of these. The number having all the three is
- a)360
- b)300
- c)380
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Out of 2000 employees in an office 48% preferred Coffee (c), 54% liked...
Total = 2000 = 100 %
C = 48 %
T = 54 %
S = 64 %
C ∩ T = 28 %
T ∩ S = 32%
C ∩ S = 30 %
Having all three = C ∩ T ∩ S = ?
None = 6 %
Total = C + T + S - C ∩ T - T ∩ S - C ∩ S + C ∩ T ∩ S + None
=> 100 = 48 + 54 + 64 - 28 - 32 - 30 + C ∩ T ∩ S + 6
=> C ∩ T ∩ S = 18 %
18 % of 2000 = (18/100) * 2000 = 360
360 having all the three
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Out of 2000 employees in an office 48% preferred Coffee (c), 54% liked...
Given data:
Total number of employees = 2000
Preference for Coffee (C) = 48%
Preference for Tea (T) = 54%
Preference for Smoking (S) = 64%
Number of employees who use C and T = 28%
Number of employees who use T and S = 32%
Number of employees who use C and S = 30%
Number of employees who do not use any of these = 6%
To find:
Number of employees who use all three, i.e., C, T, and S.
Solution:
Let's first find the number of employees who use only one or two of the three.
Number of employees who use only C = (48% - 28%) = 20%
Number of employees who use only T = (54% - 28%) = 26%
Number of employees who use only S = (64% - 32%) = 32%
Number of employees who use both C and T (but not S) = 28% - 20% = 8%
Number of employees who use both T and S (but not C) = 32% - 26% = 6%
Number of employees who use both C and S (but not T) = 30% - 20% = 10%
Number of employees who use exactly one of the three = 20% + 26% + 32% = 78%
Number of employees who use exactly two of the three = 8% + 6% + 10% = 24%
Now, let's use the given information that 6% of employees do not use any of the three.
Number of employees who use none of C, T, and S = 6%
Number of employees who use at least one of C, T, and S = 100% - 6% = 94%
Using the principle of inclusion-exclusion, we can find the number of employees who use all three:
Number of employees who use all three = Total - (Number who use exactly one) - (Number who use exactly two) - (Number who use none of the three)
= 2000 - (78% of 2000) - (24% of 2000) - (6% of 2000)
= 2000 - 1560 - 480 - 120
= 840
Therefore, the number of employees who use all three, i.e., C, T, and S, is 840.
Answer: (A) 360
Total number of employees = 2000
Preference for Coffee (C) = 48%
Preference for Tea (T) = 54%
Preference for Smoking (S) = 64%
Number of employees who use C and T = 28%
Number of employees who use T and S = 32%
Number of employees who use C and S = 30%
Number of employees who do not use any of these = 6%
To find:
Number of employees who use all three, i.e., C, T, and S.
Solution:
Let's first find the number of employees who use only one or two of the three.
Number of employees who use only C = (48% - 28%) = 20%
Number of employees who use only T = (54% - 28%) = 26%
Number of employees who use only S = (64% - 32%) = 32%
Number of employees who use both C and T (but not S) = 28% - 20% = 8%
Number of employees who use both T and S (but not C) = 32% - 26% = 6%
Number of employees who use both C and S (but not T) = 30% - 20% = 10%
Number of employees who use exactly one of the three = 20% + 26% + 32% = 78%
Number of employees who use exactly two of the three = 8% + 6% + 10% = 24%
Now, let's use the given information that 6% of employees do not use any of the three.
Number of employees who use none of C, T, and S = 6%
Number of employees who use at least one of C, T, and S = 100% - 6% = 94%
Using the principle of inclusion-exclusion, we can find the number of employees who use all three:
Number of employees who use all three = Total - (Number who use exactly one) - (Number who use exactly two) - (Number who use none of the three)
= 2000 - (78% of 2000) - (24% of 2000) - (6% of 2000)
= 2000 - 1560 - 480 - 120
= 840
Therefore, the number of employees who use all three, i.e., C, T, and S, is 840.
Answer: (A) 360
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Out of 2000 employees in an office 48% preferred Coffee (c), 54% liked (T), 64% used to smoke (S). Out of the total 28% used C and T, 32% used T and S and 30% preferred C and S, only 6% did none of these. The number having all the three isa)360b)300c)380d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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