Calculating the Fifth Friend's Bill Amount

This problem involves calculating an unknown value based on the average amount paid by a group.

Average Calculation Principle

The average is calculated as the total sum divided by the number of items. In this case:

$ \text{Average Bill} = \frac{\text{Total Bill Amount}}{\text{Number of Friends}} $

Step-by-Step Solution

• Identify Given Information:
  • Number of friends: 5
  • Amount paid by 4 friends: 4 \(\times\) Rs. 200 = Rs. 800
  • Amount paid by the fifth friend: Rs. \(x\)
  • Average bill per person: Rs. 210
• Calculate Total Bill Amount:

  Using the average formula, the total bill is:

  $ \text{Total Bill Amount} = \text{Average Bill} \times \text{Number of Friends} $

  $ \text{Total Bill Amount} = 210 \times 5 = 1050 $ So, the total bill was Rs. 1050.

• Determine the Value of \(x\):

  The total bill is the sum of the amounts paid by all friends:

  $ \text{Total Bill Amount} = (\text{Amount paid by 4 friends}) + (\text{Amount paid by fifth friend}) $

  $ 1050 = 800 + x $

  Solve for \(x\):

  $ x = 1050 - 800 $

  $ x = 250 $

Therefore, the fifth friend paid Rs. 250.