Iift 2010 Question 17
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IIFT 2010
Let the number of professors, associate professors and assistant professors be x, y and z respectively and their average ages be a, b
and c respectively.
xa + yb + zc = 2160 -------------------(1)
Average age =36
x+y+z=60
xa + yb = 39 (x + y)
3sinx + 3cosx
2
2(3 ) 2
−1
31− 2
1
≥
2
3sinx + 3cosx
≥ 3sinx ∗ 3cosx
⇒3sinx + 3cosx ≥ 2 ∗ 3 2
sinx+cosx
A2 + B2 ≤ ≤ A2 + B2
12 + 12 ≤ ≤ 12 + 12
⇒ 2 ≤ ≤ 2
2
⇒3sinx + 3cosx ≥ 2 ∗ 3 2
− 2
⇒3sinx + 3cosx ≥ 2 ∗ 3 2
−1
32 11
8
363 2
∴ 11(yb + zc) = 360(y + z)
3(xa + zc) = 110(x + z)
x(a + 1) + y(b + 6) + z(c + 7) = 2160 + 5*(60) -------(2) [ Average increases by 5]
Eq 2- Eq 1
We get x+6y+7z=300
Lets solve the options one by one
Option A: x = 16 , y = 24, z = 20
16+6*24+7*20=300 which satisfies the equations.
So either A or C can be the answer.
Now check for the values of a, b, c
a=45, b=35, c=30
ax+by+cz = 45*16+35*24+30*20
=2160
Hence, option A is the correct answer.