The result of an exam is given below
Out of 2000 students who appeared
(1) 1316 failed in Telugu
(i) 332 failed in Telugu and Punjabi
(i) 744 failed in Punjabi, 868 failed in Telugu and Bengali
(iv) 1180 failed in Bengali, 252 failed in Bengali and Punjabi
The number of students who failed in all the three subjects is?
Answers
Given :
2000 students appeared
1316 failed in Telugu
744 failed in Punjabi
1180 failed in Bengali,
332 failed in Telugu and Punjabi
868 failed in Telugu and Bengali
252 failed in Bengali and Punjabi
To Find : The number of students who failed in all the three subjects
Solution :
Assuming each student failed in atleast one subject
Failed in all 3 subjects = x
from the venn Diagram
Failed in Telegu only = 1316 - 332 - 868 + x = 116 + x
Failed in Punjabi only = 160+x
Failed in Bengali only = 60 + x
Failed in Telugu and Punjabi only = 332-x
Failed in Bengali and Punjabi only = 252-x
Failed in Telugu and Bengali only = 868-x
Failed in All three = x
Total = 2000
=> 116 + x + 160 +x + 60 + x + 332- x + 252 - x + 868 - x + x = 2000
=> 1788 + x = 2000
=> x= 212
Failed in All 3 subjects = 212 ( Assuming every one failed in atleast one subject)
If Number of students who failed in none subjects are given then those to be subtracted from 212
Correct option is 212.
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