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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


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 3rd Jan, 2024

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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