Eight out of nine persons each spend Rs 30 on their meals. The ninth person spends Rs 20 more than the average expenditure of all the nine persons. What is the total amount of money spent by all nine persons together?

Introduction / Context:
This word problem mixes average expenditure with a condition involving one person spending more than that average. You are told that eight people spend the same amount, and the ninth person spends Rs 20 more than the overall average. The task is to determine the total expenditure of all nine people by setting up and solving an equation involving the average.

Given Data / Assumptions:

• Number of persons = 9.
• Eight persons each spend Rs 30.
• Ninth person spends (average expenditure of all nine + Rs 20).
• Let the average expenditure be A rupees.
• We need to find the total expenditure of all nine persons.

Concept / Approach:
Let A be the average spending per person. Then the ninth person spends A + 20 rupees. The total spending is thus: 8 * 30 + (A + 20). But the total can also be written as 9A because the average is A over 9 people. Equating these two expressions for total expenditure allows us to solve for A and then compute the total amount.

Step-by-Step Solution:
Step 1: Let average expenditure per person = A rupees. Step 2: Expenditure of 8 persons = 8 * 30 = Rs 240. Step 3: Expenditure of 9th person = A + 20. Step 4: Total expenditure = 240 + (A + 20) = 260 + A. Step 5: But by definition of average, total expenditure also equals 9A. So, 260 + A = 9A. Step 6: Rearranging: 260 = 9A - A = 8A. Step 7: Therefore, A = 260 / 8 = 32.5 rupees. Step 8: Total expenditure = 9A = 9 * 32.5 = 292.5 rupees.
Verification / Alternative check:
Check the ninth person's expenditure: A + 20 = 32.5 + 20 = 52.5 rupees. Total expenditure = 8 * 30 + 52.5 = 240 + 52.5 = 292.5 rupees. Average = 292.5 / 9 = 32.5 rupees, which matches A and satisfies the condition that the ninth person spends Rs 20 more than the average.
Why Other Options Are Wrong:
Options B (Rs. 297.50), C (Rs. 298) and D (Rs. 298.50) correspond to averages different from Rs 32.5 and do not satisfy the relationship that the ninth person spends A + 20. Option E (Rs. 300) would give an average of 300 / 9 ≈ 33.33, so the ninth person would need to spend approximately Rs 53.33, not Rs 20 more than 33.33 exactly.
Common Pitfalls:
Some students treat Rs 20 as added to one of the known 30 rupee amounts instead of to the average, which changes the equation incorrectly. Others forget to express the total as 9A and instead equate the wrong expressions.
Final Answer:
The total money spent by all nine persons is Rs. 292.50.