47. A class of 60 students appreared for an examination of Mercan-
tile law, Statistics and Accountancy. 25 students failed in Mercantile
law, 24 failed in Statistics, 32 failed in Accountancy, 9 failed in Mercantile
Jaw alone. 6 failed in Statistics alone ; 5 failed in Accountancy and
Statistics only and 3 failed in Mercantile law and Statistics only. Find
(i) how many failed in all three subjects.
(ii) how many passed in all the three subjects.
if
Answers
Given : 25 students failed in Mercantile law, 24 failed in Statistics, 32 failed in Accountancy, 9 failed in Mercantile law alone, 6 failed in Statistics alone ; 5 failed in Accountancy and Statistics only and 3 failed in Mercantile law and Statistics only
To Find : (i) how many failed in all three subjects.
(ii) how many passed in ail the three subjects.
Solution:
Failed in Mercantile law L = 25 => Passed in Mercantile law = 35
Failed in Statistics S = 24 => Passed in Statistics = 36
Failed in Accountancy A = 32 => Passed in Accountancy = 28
failed in Mercantile law alone = 9
failed in Statistics alone = 6
failed in Accountancy and Statistics only = 5
failed in Mercantile law and Statistics only = 3
Failed in all three subjects = L ∩ S ∩ A
failed in Mercantile law alone = L - L∩ S - L ∩ A + L ∩ S ∩ A = 9
=> 16 + L ∩ S ∩ A = L∩ S + L ∩ A
failed in Statistics alone = S - L∩ S - S ∩ A + L ∩ S ∩ A = 6
=> 18 + L ∩ S ∩ A = L∩ S + S ∩ A
failed in Accountancy and Statistics only = S ∩ A - L ∩ S ∩ A = 5
S ∩ A = L ∩ S ∩ A+ 5
18 + L ∩ S ∩ A = L∩ S + S ∩ A
=> 18 + L ∩ S ∩ A = L∩ S + L ∩ S ∩ A+ 5
=> L∩ S = 13
failed in Mercantile law and Statistics only = L∩ S - L ∩ S ∩ A = 3
=> L∩ S = L ∩ S ∩ A+ 3
16 + L ∩ S ∩ A = L∩ S + L ∩ A
=> 16 + L ∩ S ∩ A = L ∩ S ∩ A+ 3 + L ∩ A
=> L ∩ A = 13
16 + L ∩ S ∩ A = L∩ S + L ∩ A
=> 16 + L ∩ S ∩ A = 13 + 13
=> L ∩ S ∩ A = 10
failed in all three subjects. = 10
Failed in Mercantile law and accountancy only = L ∩ A - L ∩ S ∩ A
= 13 - 10
=3
S ∩ A = L ∩ S ∩ A+ 5 = 10 + 5 = 15
Failed in accountancy only = A - A∩ S - L ∩ A + L ∩ S ∩ A
= 32 - 15 - 13 + 10 = 14
Failed in any of the subject = 9 + 6 + 14 + 3 + 5 + 3 + 10
= 50
Passed in all three subjects = Not failed in a any subject
= 60 - 50 = 10
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