Out of four numbers , the average of first three number is thrice the fourth number . If the average of the four numbers is 5, the fourth number is :

Options

A. 4.5
B. 5
C. 2
D. 4

Answer

To find the fourth number based on the given conditions, we can follow these steps:

1. **Understanding the Problem**: We have four numbers, let's denote them as \( a, b, c, \) and \( d \). The average of the first three numbers \( (a, b, c) \) is three times the fourth number \( d \). Additionally, the average of all four numbers is 5.

2. **Setting Up the Equations**:
- The average of the first three numbers is given by:
\[ \frac{a + b + c}{3} = 3d \]
- The average of all four numbers is:
\[ \frac{a + b + c + d}{4} = 5 \]

3. **Expressing the Sums**:
- From the second equation, we can express the sum of all four numbers:
\[ a + b + c + d = 4 \times 5 = 20 \]

4. **Substituting the First Equation**:
- From the first equation, we can express \( a + b + c \):
\[ a + b + c = 9d \quad (\text{since } 3d \times 3 = 9d) \]

5. **Combining the Equations**:
- Now we can substitute \( a + b + c \) into the sum of all four numbers:
\[ 9d + d = 20 \]
- This simplifies to:
\[ 10d = 20 \]

6. **Solving for \( d \)**:
- Dividing both sides by 10 gives:
\[ d = \frac{20}{10} = 2 \]

Thus, the fourth number \( d \) is **2**.