The mean of a, b, and c is same as the mean of b, c, and d. Then which of the following is correct?

Options

A. `a = b = c `
B. `b = c =a`
C. ` b = c `
D. `a = d`

Answer

To solve the problem step by step, we will start by understanding the concept of mean and then apply it to the given situation.

### Step-by-Step Solution:

1. **Understanding the Mean**:
The mean (average) of a set of numbers is calculated by taking the sum of all the numbers and dividing it by the count of numbers.

2. **Mean of a, b, and c**:
We calculate the mean of the numbers a, b, and c:
\[ \text{Mean of } (a, b, c) = \frac{a + b + c}{3} \]

3. **Mean of b, c, and d**:
Next, we calculate the mean of the numbers b, c, and d:
\[ \text{Mean of } (b, c, d) = \frac{b + c + d}{3} \]

4. **Setting the Means Equal**:
According to the problem, the mean of (a, b, c) is the same as the mean of (b, c, d). Therefore, we can set the two expressions equal to each other:
\[ \frac{a + b + c}{3} = \frac{b + c + d}{3} \]

5. **Eliminating the Denominator**:
We can eliminate the denominator (3) by multiplying both sides of the equation by 3:
\[ a + b + c = b + c + d \]

6. **Simplifying the Equation**:
Now, we can simplify the equation by subtracting b and c from both sides:
\[ a = d \]

7. **Conclusion**:
From the above steps, we conclude that \( a \) is equal to \( d \). Therefore, the correct answer is that \( a = d \).