Question

In our coaching, there were 200 students enrolled for DI, 150 for English and 150 for Maths. Out of these, 80 students enrolled for both DI and English, 60 students enrolled for Maths and English, while 70 students enrolled for DI and Maths. Some of these students are enrolled for DI classes only. Priyanka teaches those students who are enrolled for English only and Varun teaches students who are enrolled for Maths only. Sarvesh is the senior most faculty therefore, he can teach all the three subjects. Students always prefer a specialist for their respective subjects. If Diwakar teaches 80 students then the other three faculties can be arranged in terms of the number of students taught as:

• A. Sarvesh > Varun > Priyanka
• B. Sarvesh > Priyanka >Varun
• C. Varun > Sarvesh >Priyanka
• D. None of these

Answer 1

The correct option is A Sarvesh > Varun > Priyanka

a + x + k + z = 200 . . . (1)
b + x + k + y = 150 . . . (2)
c + y + k + z = 150 . . . (3)
But since Diwakar teaches only 80 students of DI.
Therefore, a = 80

Hence, x + k + z = 120
but (x + k) + (k + z) = 150
$\therefore$ k = 30
Hence, x = 50, z = 40, y = 30, b = 40

$\therefore$ No. of students taught by Diwakar = a = 80
No. of students taught by Priyanka = b = 40
No. of students taught by Varun = c= 50
No. of students taught by Sarvesh = x + y + z + k = 150