The average of five numbers is 6 1.4 The average of first and second number is 40.5 and that of fourth and fifth number is 72. What is the third number?

Options

A. 85
B. 83
C. 87
D. None of these

Answer

To find the third number (C) given the conditions of the problem, we can follow these steps:

### Step 1: Calculate the total sum of the five numbers.
The average of five numbers is given as 61.4. Therefore, the total sum of these five numbers (A, B, C, D, E) can be calculated using the formula for average:

\[ \text{Average} = \frac{A + B + C + D + E}{5} \]

Thus, we have:

\[ A + B + C + D + E = 61.4 \times 5 = 307 \]

### Step 2: Set up the equation for the first and second numbers.
The average of the first and second numbers (A and B) is given as 40.5. Therefore, we can write:

\[ \frac{A + B}{2} = 40.5 \]

Multiplying both sides by 2 gives us:

\[ A + B = 40.5 \times 2 = 81 \]

### Step 3: Set up the equation for the fourth and fifth numbers.
The average of the fourth and fifth numbers (D and E) is given as 72. Therefore, we can write:

\[ \frac{D + E}{2} = 72 \]

Multiplying both sides by 2 gives us:

\[ D + E = 72 \times 2 = 144 \]

### Step 4: Substitute the values into the total sum equation.
Now we have three equations:
1. \( A + B + C + D + E = 307 \) (from Step 1)
2. \( A + B = 81 \) (from Step 2)
3. \( D + E = 144 \) (from Step 3)

We can substitute equations 2 and 3 into equation 1:

\[ 81 + C + 144 = 307 \]

### Step 5: Solve for the third number (C).
Now, we can simplify the equation:

\[ C + 225 = 307 \]

Subtracting 225 from both sides gives us:

\[ C = 307 - 225 = 82 \]

### Final Answer:
The third number (C) is **82**.

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