Average of 10 numbers is 35. if average of first 5 numbers is 40 and average of last 3 numbers is 22, then what is the average of remaining two numbers?

Options

A. A)36
B. B)32
C. C)40
D. D)42

Answer

To solve the problem step by step, we will follow the calculations based on the information provided:

### Step 1: Calculate the total sum of the 10 numbers
The average of 10 numbers is given as 35.
To find the total sum of these numbers, we use the formula:
\[ \text{Total Sum} = \text{Average} \times \text{Number of Observations} \]
So,
\[ \text{Total Sum} = 35 \times 10 = 350 \]

### Step 2: Calculate the sum of the first 5 numbers
The average of the first 5 numbers is given as 40.
Using the same formula:
\[ \text{Sum of first 5 numbers} = 40 \times 5 = 200 \]

### Step 3: Calculate the sum of the last 3 numbers
The average of the last 3 numbers is given as 22.
Again, using the formula:
\[ \text{Sum of last 3 numbers} = 22 \times 3 = 66 \]

### Step 4: Set up the equation for the remaining two numbers
Let the sum of the remaining two numbers be \( P + Q \).
We can express the total sum as:
\[ \text{Total Sum} = \text{Sum of first 5} + \text{Sum of last 3} + P + Q \]
Substituting the values we calculated:
\[ 350 = 200 + 66 + P + Q \]

### Step 5: Solve for \( P + Q \)
Rearranging the equation gives:
\[ P + Q = 350 - (200 + 66) \]
Calculating the right side:
\[ P + Q = 350 - 266 = 84 \]

### Step 6: Calculate the average of the two remaining numbers
To find the average of the two numbers \( P \) and \( Q \):
\[ \text{Average of } P \text{ and } Q = \frac{P + Q}{2} = \frac{84}{2} = 42 \]

### Final Answer
The average of the remaining two numbers is **42**.

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