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The average of three numbers is 30. If one number is removed, the average become

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Question: The average of three numbers is 30. If one number is removed, the average becomes 25. What is the removed number?

Options:

  1. 35
  2. 30
  3. 25
  4. 20

Correct Answer: 35

Solution: 

Let the three numbers be x, y, z.  (x + y + z) / 3 = 30 => x + y + z = 90. After removing one number, (x + y) / 2 = 25 => x + y = 50. Therefore, removed number = 90 - 50 = 40.

The average of three numbers is 30. If one number is removed, the average become

Practice Questions

Q1
The average of three numbers is 30. If one number is removed, the average becomes 25. What is the removed number?
  1. 35
  2. 30
  3. 25
  4. 20

Questions & Step-by-Step Solutions

The average of three numbers is 30. If one number is removed, the average becomes 25. What is the removed number?
  • Step 1: Understand that the average of three numbers is 30. This means if you add the three numbers together and divide by 3, you get 30.
  • Step 2: To find the total of the three numbers, multiply the average (30) by 3. So, 30 * 3 = 90. This means x + y + z = 90.
  • Step 3: When one number is removed, the average of the remaining two numbers becomes 25. This means if you add the two remaining numbers and divide by 2, you get 25.
  • Step 4: To find the total of the two remaining numbers, multiply the new average (25) by 2. So, 25 * 2 = 50. This means x + y = 50.
  • Step 5: Now, you have two equations: x + y + z = 90 and x + y = 50.
  • Step 6: To find the removed number (z), subtract the total of the two remaining numbers (50) from the total of all three numbers (90). So, 90 - 50 = 40.
  • Step 7: Therefore, the removed number is 40.
  • Average Calculation – Understanding how to calculate the average of a set of numbers and how removing a number affects the average.
  • Algebraic Manipulation – Using algebra to set up equations based on the information given in the problem.
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