There are 35 students in a hostel. When the number of students increases by 7, the daily expense of the mess increases by Rs 42, while the average expense per head decreases by Re 1. What was the original daily expense of the mess?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 420
The total expense is the expense per head multiplied by the number of students. Writing the new total in two ways gives one equation in the old expense per head.
Let the original expense per head be Rs \(x\); original total \(=35x\)
New number of students \(=35+7=42\); new expense per head \(=x-1\)
New total \(=42(x-1)\), and also \(=35x+42\)
\(42x-42=35x+42\), so \(7x=84\) and \(x=12\)
Original daily expense \(=35\times12=420\)
The original daily expense of the mess was Rs 420 (the new expense is \(42\times11=\) Rs 462, which is Rs 42 more).