There were 35 students in a hostel. If the number of the students is increased by 7, then the expenses of the mess increased by Rs. 42 per day, while the average expenditure per head diminishes by Rs. 1. The original expenditure of the mess per day was-

Let the original expenditure of the mess per day be Rs. x
Then, new expenditure
= Rs. (x + 42)
$$\eqalign{ & \therefore \frac{x}{{35}} - \frac{{\left( {x + 42} \right)}}{{42}} = 1 \cr & \Rightarrow 6x - 5\left( {x + 42} \right) = 210 \cr & \Rightarrow x - 210 = 210 \cr & \Rightarrow x = 420 \cr} $$