NYC5648 wrote:

The expenses of a hostel are partly fixed and partly variable. It costs $120 per head per day if there are 20 students and $110 per head per day if there are 25 students. What will be the cost per head per day if the number of students increases to 40?

A. 105

B. 100

C. 95

D. 80

E. 75

Say the fixed cost is \($x\) and the variable cost is \($y\) per head. Then:

\(cost \ per \ head=\frac{total \ cost}{# \ of \ students}=\frac{x+20y}{20}=120\) --> \(x+20y=20*120\);

\(cost \ per \ head=\frac{total \ cost}{# \ of \ students}=\frac{x+25y}{25}=110\) --> \(x+25y=25*110\);

Subtract the first equation from the second: \(5y=25*110-20*120\) --> \(y=70\) --> \(x=1,000\).

Therefore the cost per head per day for 40 students will be \(\frac{x+40y}{y}=\frac{1,000+40*70}{40}=95\).

Answer: C.

Because he's the hero GMATclub Needs, but don't deserve. So, we'll ask him 700level questions, because he can take it. He's a silent guardian. A watchful protector. A Bunuel.

(in case you didn't notice it, I modified a quote from the movie "The dark Night"