The average of a b and c is 20 and that of b, c and d is 25. If d = 30, then the value of a is :

Options

A. 25
B. 45
C. 30
D. 15

Answer

To solve the problem step by step, let's break it down:

1. **Understand the given information**:
- The average of A, B, and C is 20.
- The average of B, C, and D is 25.
- The value of D is 30.

2. **Set up the equations based on the averages**:
- The average of A, B, and C can be expressed as:
\[ \frac{A + B + C}{3} = 20 \]
Multiplying both sides by 3 gives:
\[ A + B + C = 60 \quad \text{(Equation 1)} \]

- The average of B, C, and D can be expressed as:
\[ \frac{B + C + D}{3} = 25 \]
Multiplying both sides by 3 gives:
\[ B + C + D = 75 \quad \text{(Equation 2)} \]

3. **Substitute the value of D into Equation 2**:
- Since D = 30, we can substitute this value into Equation 2:
\[ B + C + 30 = 75 \]
Subtracting 30 from both sides gives:
\[ B + C = 45 \quad \text{(Equation 3)} \]

4. **Substitute Equation 3 into Equation 1**:
- Now we can substitute Equation 3 into Equation 1:
\[ A + (B + C) = 60 \]
Replacing \(B + C\) with 45 from Equation 3 gives:
\[ A + 45 = 60 \]

5. **Solve for A**:
- Subtracting 45 from both sides gives:
\[ A = 60 - 45 \]
Therefore:
\[ A = 15 \]

Thus, the value of A is **15**.