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

Introduction:
This problem uses the idea of averages where one part of the group spends a fixed amount and the remaining members spend an amount defined in terms of the overall average. It is a classic example of solving an equation where the average itself is unknown.

Given Data / Assumptions:
Total number of friends = 19. Number of friends in the first group = 13, each spending Rs 79. Number of remaining friends = 19 - 13 = 6. Each of these 6 friends spends Rs 4 more than the overall average expenditure of all 19 friends. We need the total money spent by all 19 friends.

Concept / Approach:
Let the average expenditure of all 19 friends be A rupees. Then: Total spending by 19 friends = 19 * A. Spending of the first 13 friends = 13 * 79. Spending of each of the remaining 6 friends = A + 4. We equate the sum of these two parts to 19 * A and solve for A, then find the total expenditure.

Step-by-Step Solution:
Step 1: Assume the overall average expenditure is A rupees. Step 2: Total expenditure of the 13 friends = 13 * 79 = 1027 rupees. Step 3: Total expenditure of the other 6 friends = 6 * (A + 4). Step 4: Total expenditure of all 19 friends = 19 * A. Step 5: Form the equation: 13 * 79 + 6 * (A + 4) = 19 * A. That is, 1027 + 6A + 24 = 19A. So, 1051 + 6A = 19A. 13A = 1051. A = 1051 / 13 ≈ 80.846 rupees. Step 6: Total money spent = 19 * A = 19 * (1051 / 13) = 19969 / 13 ≈ Rs 1536.07.

Verification / Alternative Check:
You can approximate mentally: since 13 people spend 79 each, their total is about 13 * 80 = 1040 (slightly less in reality). If the average is a bit above 80, total for 19 people should be slightly more than 19 * 80 = 1520, which is consistent with Rs 1536.07.

Why Other Options Are Wrong:
Rs 1398.96 and Rs 1457.09: These are too low compared to 19 people spending around Rs 80 on average. Rs 1662.35 and Rs 1601.50: These are too high and would imply an average much larger than the values derived from the equation.

Common Pitfalls:
Many learners incorrectly assume the 6 friends spend Rs 4 more than Rs 79, instead of Rs 4 more than the overall average A. Another pitfall is forgetting that the total expenditure must be 19 * A, not a simple sum of the known fixed amounts. Always express all unknown parts in terms of A, build a single equation, and then solve.

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