Question:
The average of five numbers is 10. If one of the numbers is 12, what is the average of the remaining four numbers?
The average of five numbers is 10. If one of the numbers is 12, what is the average of the remaining four numbers?
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In average problems, it's almost always helpful to first calculate the total sum. Working with sums is often more straightforward than trying to manipulate the averages directly.
Updated On: Oct 4, 2025
- 9.5
- 10
- 8
- 11
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The average (or mean) of a set of numbers is their sum divided by the count of numbers. We can use this relationship to find the sum of the numbers, and then work backwards to find the average of the subset.
Step 2: Key Formula or Approach:
\[ \text{Sum} = \text{Average} \times \text{Count} \] Step 3: Detailed Explanation:
Step 3a: Find the sum of the original five numbers.
The average of five numbers is 10.
\[ \text{Sum of five numbers} = 10 \times 5 = 50 \] Step 3b: Find the sum of the remaining four numbers.
One of the numbers is 12. We can remove this from the sum.
\[ \text{Sum of remaining four numbers} = (\text{Sum of five numbers}) - 12 \] \[ \text{Sum of remaining four numbers} = 50 - 12 = 38 \] Step 3c: Find the average of the remaining four numbers.
There are now four numbers, and their sum is 38.
\[ \text{Average of remaining four numbers} = \frac{\text{Sum of four numbers}}{4} \] \[ \text{Average} = \frac{38}{4} = 9.5 \] Step 4: Final Answer:
The average of the remaining four numbers is 9.5.
The average (or mean) of a set of numbers is their sum divided by the count of numbers. We can use this relationship to find the sum of the numbers, and then work backwards to find the average of the subset.
Step 2: Key Formula or Approach:
\[ \text{Sum} = \text{Average} \times \text{Count} \] Step 3: Detailed Explanation:
Step 3a: Find the sum of the original five numbers.
The average of five numbers is 10.
\[ \text{Sum of five numbers} = 10 \times 5 = 50 \] Step 3b: Find the sum of the remaining four numbers.
One of the numbers is 12. We can remove this from the sum.
\[ \text{Sum of remaining four numbers} = (\text{Sum of five numbers}) - 12 \] \[ \text{Sum of remaining four numbers} = 50 - 12 = 38 \] Step 3c: Find the average of the remaining four numbers.
There are now four numbers, and their sum is 38.
\[ \text{Average of remaining four numbers} = \frac{\text{Sum of four numbers}}{4} \] \[ \text{Average} = \frac{38}{4} = 9.5 \] Step 4: Final Answer:
The average of the remaining four numbers is 9.5.
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