Out of four numbers the average of the first three is 16 and that of the last three is 15. If the last number Is 20 then the first number is:

Options

A. 23
B. 25
C. 28
D. 21

Answer

To solve the problem step by step, we will follow the information provided and use the formulas for averages.

### Step 1: Define the variables
Let the four numbers be \( A, B, C, \) and \( D \).

### Step 2: Set up the equations based on the averages
1. The average of the first three numbers \( A, B, C \) is 16:
\[ \frac{A + B + C}{3} = 16 \]
Multiplying both sides by 3 gives:
\[ A + B + C = 48 \quad \text{(Equation 1)} \]

2. The average of the last three numbers \( B, C, D \) is 15:
\[ \frac{B + C + D}{3} = 15 \]
Multiplying both sides by 3 gives:
\[ B + C + D = 45 \quad \text{(Equation 2)} \]

### Step 3: Substitute the value of \( D \)
We know that \( D = 20 \). Substituting this into Equation 2:
\[ B + C + 20 = 45 \]
Subtracting 20 from both sides gives:
\[ B + C = 25 \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 3 into Equation 1
Now we can substitute Equation 3 into Equation 1:
\[ A + (B + C) = 48 \]
Replacing \( B + C \) with 25:
\[ A + 25 = 48 \]
Subtracting 25 from both sides gives:
\[ A = 48 - 25 \]
Thus,
\[ A = 23 \]

### Conclusion
The first number \( A \) is 23.

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