Seven friends each spent Rs 14 on a project, and an eighth friend spent Rs 21 more than the average expenditure of all eight friends together. What is the total amount of money (in rupees) spent by the eight friends on the project?

Introduction / Context:
This question involves a slightly circular average situation. Seven friends spend a fixed known amount each. The eighth friend spends an amount defined in terms of the overall average of all eight, not as a fixed number. We are asked to find the total expenditure of all eight friends. To do this, we must set up an equation where the average itself is an unknown and the eighth friend's spending depends on that unknown average.

Given Data / Assumptions:

• Seven friends each spend Rs 14.
• The eighth friend spends Rs 21 more than the average expenditure of all eight friends together.
• Let the average expenditure of all eight be A rupees.
• We need to find the total amount spent by all eight friends.

Concept / Approach:
If the average expenditure is A, then the total expenditure is 8A. We know seven of the friends each spend 14, so their combined spending is 7 * 14. The eighth friend spends A + 21. Therefore, total expenditure can also be written as 7 * 14 + (A + 21). Since both expressions represent the same total, we equate 8A to this sum and solve for A. Once A is known, we can compute the total expenditure as 8A directly.

Step-by-Step Solution:
Step 1: Let A be the average expenditure of all eight friends. Step 2: Total expenditure in terms of A is 8A. Step 3: Compute the spending of the seven friends. Seven friends spend 14 each, so total for seven friends = 7 * 14 = 98. Step 4: Express the eighth friend's spending. Eighth friend spends A + 21. Step 5: Equate total expenditure from both viewpoints. 8A = 98 + (A + 21). 8A = 98 + A + 21 = 119 + A. Step 6: Solve for A. 8A − A = 119. 7A = 119. A = 119 / 7 = 17. Step 7: Find the total expenditure. Total = 8A = 8 * 17 = 136.
Verification / Alternative check:
Seven friends together spend 7 * 14 = 98. Average expenditure is A = 17, so the eighth friend spends A + 21 = 17 + 21 = 38. Total = 98 + 38 = 136, and 136 / 8 = 17, confirming that A is indeed the correct average.
Why Other Options Are Wrong:
Totals of 133, 141, 155 or 147 would give averages that are not consistent with the condition that the eighth friend spends exactly Rs 21 more than the average. For instance, if total were 141, average would be 141 / 8, which is not an integer and would not give a clean value for A + 21 matching the eighth friend's spending.
Common Pitfalls:
A common mistake is to assume the eighth friend spends 21 more than the other friends, rather than 21 more than the overall average. Another error is to forget that the expression for total expenditure must be set equal to 8A, not just the sum of the known amounts.
Final Answer:
The total amount of money spent by the eight friends is Rs 136.