Out of 9 persons, 8 persons spend Rs. 30 each for their meals. The ninth person spends Rs. 20 more than the average expenditure of all 9 persons. What is the total money spent by all of them?

Introduction / Context:
This question is a classic average and total expenditure problem. You know the expenditure of eight persons and are given a special condition about how much the ninth person spends relative to the overall average. Using this information, you must work backwards to find the average expenditure and then the total money spent by all nine persons. This type of problem is frequently asked in aptitude tests.

Given Data / Assumptions:
- Number of persons = 9.
- 8 persons each spend Rs. 30.
- The ninth person spends Rs. 20 more than the average expenditure of all nine persons.
- Let the average expenditure of all nine persons be x rupees.
- We need the total expenditure by all nine persons.

Concept / Approach:
The key is to express everything in terms of the unknown average x. The total expenditure is the sum of the expenditures of the eight persons plus that of the ninth person. This total, divided by 9, must equal x. Forming an equation from this relation allows us to solve for x and then compute the total expenditure easily.

Step-by-Step Solution:
Step 1: Let the average expenditure of all nine persons be x rupees.Step 2: Total expenditure of 8 persons who each spend Rs. 30 is 8 * 30 = Rs. 240.Step 3: The ninth person spends x + 20 rupees.Step 4: Total expenditure of all nine persons = 240 + (x + 20) = 260 + x.Step 5: By definition of average, total expenditure = 9 * x.Step 6: Therefore, 9x = 260 + x.Step 7: Simplify: 9x - x = 260, so 8x = 260.Step 8: Hence x = 260 / 8 = 32.5 rupees.Step 9: Total expenditure = 9 * x = 9 * 32.5 = Rs. 292.50.

Verification / Alternative Check:
Check the condition for the ninth person. Average expenditure is Rs. 32.50, so the ninth person spends 32.50 + 20 = Rs. 52.50. Sum of expenditures of 8 persons is 8 * 30 = Rs. 240. Adding the ninth person gives 240 + 52.50 = Rs. 292.50. Dividing 292.50 by 9 again gives 32.50, confirming that the average is consistent.

Why Other Options Are Wrong:
Totals such as Rs. 297.50, Rs. 298 or Rs. 298.50 would give averages that are not equal to x when you apply the given condition about the ninth person spending x + 20. Only Rs. 292.50 ensures that the ninth person expenditure and the overall average agree with the problem statement.

Common Pitfalls:
Many students treat 20 as extra over Rs. 30 instead of extra over the average, which leads to a wrong equation. Others forget to include x inside the total on both sides. Always read the phrase carefully: more than the average expenditure of all nine persons, and then set up the equation accordingly.

Final Answer:
The total money spent by all nine persons is Rs. 292.50.