The mean of three numbers is 51. All the three numbers are different natural numbers. If two of them are 29 and 59, then find the third number.

Options

A. 65
B. 40
C. 100
D. 71

Answer

To find the third number when the mean of three numbers is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Mean**:
The mean (average) of three numbers is given as 51. The formula for the mean of three numbers \(a\), \(b\), and \(c\) is:
\[ \text{Mean} = \frac{a + b + c}{3} \]
Given that the mean is 51, we can write:
\[ \frac{a + b + c}{3} = 51 \]

2. **Finding the Sum of the Numbers**:
To find the sum of the three numbers, we can rearrange the equation:
\[ a + b + c = 51 \times 3 \]
Calculating this gives:
\[ a + b + c = 153 \]

3. **Identifying Known Values**:
We know two of the numbers are 29 and 59. Let’s denote the third number as \(X\). Therefore, we can substitute \(a\) and \(b\) in our equation:
\[ 29 + 59 + X = 153 \]

4. **Calculating the Third Number**:
First, we calculate the sum of 29 and 59:
\[ 29 + 59 = 88 \]
Now, substituting this back into the equation gives:
\[ 88 + X = 153 \]
To find \(X\), we subtract 88 from both sides:
\[ X = 153 - 88 \]
Calculating this gives:
\[ X = 65 \]

5. **Conclusion**:
The third number is 65.

### Final Answer:
The third number is **65**.