The average of 5 numbers A,B,C,D,E are 20 .The average of first 3 numbers A,B,C are 20 and last 3 numbers C,D,E are 15. find the value of C number ?

Options

A. 5
B. 8
C. 10
D. 12

Answer

To find the value of C, we can follow these steps:

1. **Calculate the total of A, B, C, D, and E**:
- Given that the average of the five numbers A, B, C, D, and E is 20, we can calculate the total sum:
\[ A + B + C + D + E = \text{Average} \times \text{Number of elements} = 20 \times 5 = 100 \]

2. **Calculate the total of A, B, and C**:
- The average of the first three numbers A, B, and C is also given as 20. Therefore, we can calculate their total:
\[ A + B + C = \text{Average} \times \text{Number of elements} = 20 \times 3 = 60 \]

3. **Calculate the total of C, D, and E**:
- The average of the last three numbers C, D, and E is given as 15. Thus, we calculate their total:
\[ C + D + E = \text{Average} \times \text{Number of elements} = 15 \times 3 = 45 \]

4. **Set up the equations**:
- Now we have three equations:
1. \( A + B + C + D + E = 100 \)
2. \( A + B + C = 60 \)
3. \( C + D + E = 45 \)

5. **Express D + E in terms of C**:
- From the first equation, we can express D + E:
\[ D + E = (A + B + C + D + E) - (A + B + C) = 100 - 60 = 40 \]

6. **Substitute D + E into the equation for C, D, and E**:
- Now we can substitute D + E into the equation for C, D, and E:
\[ C + (D + E) = 45 \implies C + 40 = 45 \]

7. **Solve for C**:
- Rearranging gives us:
\[ C = 45 - 40 = 5 \]

Thus, the value of C is **5**.