Question : There are 45 students in a hostel. If the number of students increases by 5, the total expenses of the mess increase by INR 30 per day while the average daily expenditure per head diminishes by INR 2. Find the original total daily expenditure of the mess.
Option 1: INR 1,170
Option 2: INR 1,710
Option 3: INR 1,200
Option 4: INR 1,250
Correct Answer: INR 1,170
Solution :
Given,
No. of students in a hostel = 45
When 5 students increase, the average daily expenditure per head decreases by INR 2.
Let the average expenditure initially be INR $x$
⇒ Total expenditure = $45x$
Now, when 5 more students join, total expenditure becomes $(45x + 30)$
⇒ Now, the average expenditure = $\frac{\text{Sum of values}}{\text{No. of values}}=\frac{45x + 30}{45 +5}=\frac{45x +30}{50}$
According to the question,
⇒ $\frac{45x +30}{50} = x-2$
⇒ $45x +30 = 50x - 100$
⇒ $130 = 5x$
⇒ $x=26$
⇒ Original total daily expenditure = 45 × 26 = INR 1,170
Hence, the correct answer is INR 1170.
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