In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?
Explanation:
Let Tm and Tb be total scores of the students majoring in Mathematics and Biology respectively.
According to the given conditions,
Tm = (M + 6) × 45
Tb = (B + 15) × 60
Also, (Tm + Tb) = (B + P + 21) × 50
45(M + 6) + 60(B + 15) = 50M + 50B + 1050
10B – 5M + 270 + 900 = 1050
10B – 5M = –120
M = 2B + 24
Here, we need to determine the maximum value of P.
∴ We need to minimize the value of B. Minimum value of B can be 0.
∴ M = 24
Again, we know that,
M + B + P + 21 = 60
⇒ 24 + 0 + P + 21 = 60
⇒ P = 15
Hence, option (d).
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