The average income of A, B and C is Rs. 12,000 per month and the average income of B, C and D is Rs. 15,000 per month. If the average salary of D be twice that of A, then the average salary of B and C is (in Rs.) :

Options

A. 8000
B. 18000
C. 13500
D. 9000

Answer

To solve the problem step by step, we will follow the information given in the question and derive the necessary values.

### Step 1: Understand the averages given in the question
The average income of A, B, and C is Rs. 12,000 per month. This means:
\[ \frac{A + B + C}{3} = 12,000 \]
Multiplying both sides by 3 gives:
\[ A + B + C = 36,000 \quad \text{(Equation 1)} \]

### Step 2: Analyze the second average
The average income of B, C, and D is Rs. 15,000 per month. This means:
\[ \frac{B + C + D}{3} = 15,000 \]
Multiplying both sides by 3 gives:
\[ B + C + D = 45,000 \quad \text{(Equation 2)} \]

### Step 3: Relate D to A
According to the problem, the average salary of D is twice that of A. Therefore:
\[ D = 2A \]

### Step 4: Substitute D in Equation 2
We can substitute \(D = 2A\) into Equation 2:
\[ B + C + 2A = 45,000 \]

### Step 5: Express B + C in terms of A
Now we can express \(B + C\) from the modified Equation 2:
\[ B + C = 45,000 - 2A \quad \text{(Equation 3)} \]

### Step 6: Substitute A in Equation 1
From Equation 1, we know:
\[ A + B + C = 36,000 \]
We can express \(B + C\) in terms of A:
\[ B + C = 36,000 - A \quad \text{(Equation 4)} \]

### Step 7: Set Equation 3 equal to Equation 4
Now, we can set Equation 3 equal to Equation 4:
\[ 45,000 - 2A = 36,000 - A \]

### Step 8: Solve for A
Rearranging gives:
\[ 45,000 - 36,000 = 2A - A \]
\[ 9,000 = A \]

### Step 9: Find D
Now that we have \(A\), we can find \(D\):
\[ D = 2A = 2 \times 9,000 = 18,000 \]

### Step 10: Substitute A back to find B + C
Substituting \(A\) back into Equation 1:
\[ 9,000 + B + C = 36,000 \]
\[ B + C = 36,000 - 9,000 = 27,000 \]

### Step 11: Calculate the average salary of B and C
The average salary of B and C is:
\[ \text{Average} = \frac{B + C}{2} = \frac{27,000}{2} = 13,500 \]

### Final Answer
The average salary of B and C is Rs. 13,500.

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