There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Tk. 42 per day while the average expenditure per head diminishes by Tk. 1. Find the original expenditure of the mess?

Suppose the average expenditure was Tk. a.
Then total expenditure = 35a
When 7 more students join the mess, total expenditure = 35a + 42
Now, the average expenditure= (35a + 42)/(35 + 7)

Now, we have,
(35a + 42)/42 = (a - 1)
⇒ 35a + 42 = 42a – 42
⇒ 7a = 84
⇒ a = 12
Thus the original expenditure of the mess = 35 x 12 = 420.