Solution

Given that there are 20 students in a mountain climbing camp. When the number of students increases by 5, the mess expenditure increases by ₹35 per day, and the average expenditure per head decreases by ₹3.

 

Let the original total expenditure of the camp be ₹ x.

 

The original average expenditure per head = ₹ \({x \over 2}\).

 

After the increase in students, the new total expenditure = ₹ x + 35, and the number of students = 25.

 

The new average expenditure per head = ₹\({x + 35 \over 25}\)

 

According to the problem:

\({x \over 2}\) - \({x + 35 \over 25}\) = 3

 

Simplifying:

5x − 4(x+35) = 300

x − 140 = 300

x = 440

 

Hence, the original expenditure of the camp is ₹ 440.