There were 45 students in a hostel, if the number of students increased by 7, the expenses of the mess were increased by rs. 39 per day while the average expenditure per head diminished by re.1. What is the original expenditure of the mess (in rs)?
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The original expenditure of the mess is Rs. 585 per day.
Step-by-step explanation:
Let the original average expenditure per student be Rs. “x”.
So, the total expenditure of the mess = Rs. 45x
After an increase by 7, the no. of students now become = 45 + 7 = 52
Now, according to the data in the question, we can write the eq. as,
52(x - 1) – 45x = 39
⇒ 52x - 52 – 45x = 39
⇒ 7x = 52 + 39
⇒ x = 91/7
⇒ x = Rs. 13
Thus,
The original expenditure in the mess per day would be,
= 13 * 45
= Rs. 585
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