Twenty men go to a restaurant. Nineteen of them pay Rs 70 each and the twentieth man pays Rs 90.25 more than the average amount paid by all 20 men. What is the total bill for the group?

Introduction:
This question tests your ability to work with averages when one data point is defined relative to the average itself. Nineteen men pay a fixed amount, and the last man pays some amount more than the overall average that includes his own payment. We must set up and solve an equation involving the unknown average and then find the total bill.

Given Data / Assumptions:
- Total number of men in the group = 20. - Nineteen men each pay Rs 70. - The twentieth man pays Rs 90.25 more than the average payment of all 20 men. - We must find the total bill for all 20 men together.

Concept / Approach:
Let the average payment of the 20 men be A rupees. The nineteenth men contribute a fixed amount, and the twentieth man contributes A + 90.25. The total bill is the sum of all individual payments, which is also equal to 20A because A is the average. By equating these two expressions, we can solve for A and then compute the total bill 20A.

Step-by-Step Solution:
Step 1: Let A be the average amount paid by each of the 20 men. Step 2: Payment by each of the nineteen men = Rs 70, so total from these nineteen men = 19 * 70 = 1330. Step 3: Payment by the twentieth man = A + 90.25. Step 4: Total bill T can be written as T = 1330 + (A + 90.25). Step 5: By definition of average, T is also equal to 20A. Step 6: Therefore, 20A = 1330 + A + 90.25. Step 7: Rearrange to collect A terms: 20A - A = 1330 + 90.25. Step 8: This gives 19A = 1420.25. Step 9: Solve for A: A = 1420.25 / 19 = 74.75. Step 10: Total bill T = 20A = 20 * 74.75 = 1495.

Verification / Alternative Check:
Check the twentieth man payment. If A = 74.75, he pays A + 90.25 = 74.75 + 90.25 = 165. The nineteen men pay a total of 1330, so the total bill is 1330 + 165 = 1495. The average from this total is 1495 / 20 = 74.75, which matches A, so the calculation is consistent.

Why Other Options Are Wrong:
Options Rs 548, Rs 850, Rs 1750 and Rs 1400 do not satisfy the condition that the twentieth man pays Rs 90.25 more than the average of all 20 men. Substituting these totals and recomputing the implied average leads to contradictions with the problem statement.

Common Pitfalls:
A common mistake is to assume the twentieth man pays Rs 90.25 more than 70, rather than more than the overall average. Another error is to forget that the total is equal to 20A and only count the nineteen men payments. Always connect the average back to the total sum via total = average * number of items.

Final Answer:
The total bill for the group of 20 men is Rs 1495.