In a class of 50 students, 25 passed in Physics, 27 in Maths, 29 in Chemistry, 33 in Biology and 35 students passed in Geography. What is the maximum number of students who passed in at least 3 subjects?
explaination isn't clear

could you explain the second equation, a+2b+3c+4d+5e=149? How did you get this equation?

Hi Himanshu,

Let the number of students who pass in exactly one subject be a, exactly 2 be b, exactly 3 be c, exactly 4 be d and exactly 5 be e.

a+b+c+d+e = 50
a+2b+3c+4d+5e = 25+27+29+33+35 = 149

We have to get the maximum number of students who passed in at least three subjects, i.e. we have to maximize c+d+e.

From the 2 equations, we have, b+2c+3d+4e = 99.
So, b+2(c+d+e)+d+2e = 99. b =1 and c = 49 and d = e = a = 0 => c + d + e = 49 is the maximum value.

Please let us know which part is not clear. We will try to explain that in greater detail.