Twenty men went to a restaurant. Nineteen of them paid Rs. 70 each. The twentieth man paid Rs. 90.25 more than the average amount paid by all 20 men. What was the total bill for the group?

Introduction / Context:
This problem is a slightly tricky average and total cost question. Most people in the group pay the same amount, but one person pays more than the overall average. You must use this information to determine the total bill. The key is to set up an equation involving the unknown average and then solve for it and the total.

Given Data / Assumptions:

• Total number of men = 20.
• Nineteen men each pay Rs. 70.
• The twentieth man pays Rs. 90.25 more than the average amount paid by all 20 men.
• The average amount per man is unknown and must be found as part of the solution.
• We must compute the total bill for all 20 men.

Concept / Approach:
Let the average amount paid per man be x rupees. Then the twentieth man's payment is x + 90.25. The sum of all payments is the sum from the 19 men paying Rs. 70 each plus the amount paid by the twentieth man. But the sum of all payments is also equal to 20x, because x is the average over 20 men. Therefore we can write an equation: 19 * 70 + (x + 90.25) = 20x, and solve for x.

Step-by-Step Solution:
Step 1: Let the average payment per man be x rupees. Step 2: Nineteen men pay 70 each, so their total is 19 * 70 = 1330. Step 3: The twentieth man pays x + 90.25. Step 4: Total of all 20 payments = 1330 + x + 90.25. Step 5: Since the average payment is x, total payment is also 20x. Step 6: Set up the equation: 1330 + x + 90.25 = 20x. Step 7: Combine like terms on the left: 1420.25 + x = 20x. Step 8: Subtract x from both sides: 1420.25 = 19x. Step 9: Solve for x: x = 1420.25 / 19. Step 10: Compute x: 19 * 74 = 1406, remainder 14.25, and 14.25 / 19 = 0.75, so x = 74.75. Step 11: Total bill = 20x = 20 * 74.75 = 1495.

Verification / Alternative check:
Check the twentieth man's payment. If the average is Rs. 74.75, then he pays 74.75 + 90.25 = 165. Now compute the total with this breakdown: 19 * 70 = 1330 and 1 * 165 = 165, giving a total of 1495. The average of 1495 over 20 men is 1495 / 20 = 74.75, which matches the assumed average, confirming our solution is consistent.

Why Other Options Are Wrong:
A total of Rs. 548 or Rs. 850 is far too small for 20 men paying around Rs. 70 or more each. A total of Rs. 1750 would correspond to a different average and would not match the condition that the last man pays exactly Rs. 90.25 more than the average. The option Rs. 1325 also does not yield a consistent average. Only Rs. 1495 produces an average of Rs. 74.75, with the last man paying Rs. 165.

Common Pitfalls:
Some students try to guess the total bill without using an equation, or they misinterpret the phrase 'more than the average' and add Rs. 90.25 to 70 instead of to the unknown average. Another common error is to forget to multiply the average by 20 when relating it to the total. Writing down the equation 1330 + x + 90.25 = 20x clearly and solving step by step is the safest approach.

Final Answer:
The total bill paid by the 20 men was Rs. 1495.