in a college of 525 students, each student takes at least two items from among idly,dosa, puri, and chapathi?

Question

for his breakfast. if 375 students take idly, 375 students take dosa , 375 students take puri and 375 students take chapatti for their breakfast, the number of students who take all the four items is at most...

options :--

275
300
225
325
375

please give detailed answer.

Answer 1

(375 + 375 + 375 + 375 - 2 * 525) / 2 = 225
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Answer 2

Answer is at the most 225 students take all items as explained below.

Let x = number of students taking all 4 items.
Then 525 - x students have to take at least 2 items.
Total items ≥ 4x + 2(525 - x)
As 375 of each item is taken, total should be less than 4 x 375 = 1500
=> 4x + 2 (525 - x) ≤Total no. of items ≤1500
=> 2x ≤1500 - 1050
=> x ≤225


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