Nineteen friends went to a restaurant for a combined weekend dinner party. Thirteen of them spent Rs 79 each on their dinner and the remaining six each spent Rs 4 more than the average expenditure of all 19 friends. What was the total amount of money spent by the group?

Introduction / Context:
This question is more challenging because the unknown average appears both in the definition of the total and inside the description of how much some people spent. It is a typical algebraic average problem where some members spend a fixed amount and the remaining ones spend an amount defined in terms of the overall average. You must set up an equation for the total expenditure in terms of the unknown average and then solve it.

Given Data / Assumptions:

• Total number of friends = 19.
• 13 friends each spent Rs 79.
• The remaining 6 friends each spent Rs 4 more than the overall average expenditure of all 19 friends.
• We are required to find the total amount spent by all 19 friends together.

Concept / Approach:
Let the average expenditure of all 19 friends be A rupees. Then the total expenditure of the group is 19A. We can also express the total expenditure as the sum of what the first 13 friends spent plus what the remaining 6 friends spent. Since each of the remaining 6 spent A + 4, their total is 6(A + 4). Equating these two expressions for the total leads to a linear equation in A that we can solve, and then we can compute 19A.

Step-by-Step Solution:
Let the overall average expenditure be A rupees.Then total expenditure of all 19 friends = 19A.Thirteen friends spent Rs 79 each, so their total expenditure = 13 * 79.Compute 13 * 79 = 1027.The remaining 6 friends each spent A + 4 rupees, so their total expenditure = 6(A + 4).Therefore, total expenditure can also be written as 1027 + 6(A + 4).Equate both expressions for total expenditure: 19A = 1027 + 6(A + 4).Expand the right side: 19A = 1027 + 6A + 24 = 1051 + 6A.Rearrange: 19A - 6A = 1051, so 13A = 1051.Hence A = 1051 / 13 ≈ 80.846 rupees.Total expenditure = 19A = 19 * 1051 / 13 = 1051 * (19 / 13) ≈ Rs 1536.07.

Verification / Alternative check:
We can verify with approximate values. If the average A ≈ 80.85, then the six friends each spent about 84.85. Total for 13 friends = 13 * 79 = 1027. Total for 6 friends ≈ 6 * 84.85 ≈ 509.1. Combined total ≈ 1536.1, which divided by 19 gives about 80.85 again. This matches A, so the calculation is self-consistent and the total of about Rs 1536.07 is correct.

Why Other Options Are Wrong:
Each other option corresponds to a different assumed average. If you work backwards from those totals and try to recompute the amounts spent by the last 6 friends as A + 4, you will find inconsistencies. The precise algebraic solution shows that only around Rs 1536.07 matches all the constraints of the problem.

Common Pitfalls:
Many students get confused because the average appears inside the expression A + 4 as well as in 19A. Some forget that the 6 friends depend on the final average, not the 13 friends' spending. Others attempt to guess the average instead of writing the equation. The safest approach is always to define A, express the total in two ways, and solve the resulting linear equation carefully.

Final Answer:
The total money spent by the 19 friends is approximately Rs 1536.07.