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?

- 30
- 25
- 20
- 15
- None of the above

**Answer**

M + P + B = 60 - (6+15+0) = 39

Sum of English Marks for Maths students = (M+6) × 45

Sum of English Marks for Biology students = (B+15) × 60

Sum of English Marks for both Maths and Biology students = (M+B+21) × 50

(M+6)×45 + (B+15)×60 = (M+B+21)×50

9M + 54 + 12B + 180 = 10M + 10B + 210

M = 2B + 24

Also, M + P + B = 39

So, 3B + P + 24 = 39

3B + P = 15

For P to be maximum,

B = 0

P = 15

**The correct option is D.**