In this question there are 260 students who are counted 160 + 130 + 110 = 380 times
This means there is an extra count of 380 – 260 = 120 students
Now, let the no. of students who choose all the three Subject be ‘n’
Then as per the question, the no. of students who choose more than 1 subject = 1.4 n
Thus, the no of students who study exactly 2 subjects = 1.4 n – n = 0.4 n
Extra count can occur from exactly 2 areas i.e from the ‘exactly two areas’ or ‘all three area’. We also know that a student placed in in all the three area will be counted 3 times, thus the extra count being 2 while in the case of exactly two students extra count is 1.
Thus the extra count from n students choose 3 subjects would be = 2 x n = 2n
And that of 0.4 student choose exactly 2 subjects = 1 x 0.4 n = 0.4n
Hence extra count = 120 = 2n + 0.4n
=) 120 = 2.4 n
=) = n
=) 50 = n
Hence the no of students who choose all the three subjects = 50
Correct Answer: 50
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