Present age of C is 9 less than the sum of present age of A & Band 6 years hence, age of B will be twice of age of A. If C is 15 years older than B, then find present age of D (present age of D is 4 less than the average of present: age of A, B & C).

Options

A. A)41 years
B. B)45 years
C. C)52 years
D. D)59 years

Answer

To solve the problem step by step, we will define the present ages of A, B, C, and D using algebraic expressions.

### Step 1: Define the variables
Let:
- A = present age of A
- B = present age of B
- C = present age of C
- D = present age of D

### Step 2: Set up the equations based on the problem statement
1. From the statement "the present age of C is 9 less than the sum of present ages of A and B":
\[ C = A + B - 9 \quad \text{(Equation 1)} \]

2. From the statement "6 years hence, age of B will be twice the age of A":
\[ B + 6 = 2(A + 6) \quad \text{(Equation 2)} \]

3. From the statement "C is 15 years older than B":
\[ C = B + 15 \quad \text{(Equation 3)} \]

### Step 3: Substitute Equation 3 into Equation 1
Substituting \( C \) from Equation 3 into Equation 1:
\[ B + 15 = A + B - 9 \]
Now, simplify this equation:
\[ 15 + 9 = A \quad \Rightarrow \quad A = 24 \quad \text{(Equation 4)} \]

### Step 4: Use Equation 4 in Equation 2
Now substitute \( A = 24 \) into Equation 2:
\[ B + 6 = 2(24 + 6) \]
Calculate the right side:
\[ B + 6 = 2(30) \quad \Rightarrow \quad B + 6 = 60 \]
Now solve for \( B \):
\[ B = 60 - 6 \quad \Rightarrow \quad B = 54 \quad \text{(Equation 5)} \]

### Step 5: Find C using Equation 3
Now substitute \( B = 54 \) into Equation 3 to find \( C \):
\[ C = 54 + 15 \quad \Rightarrow \quad C = 69 \quad \text{(Equation 6)} \]

### Step 6: Calculate the average of A, B, and C
Now we need to find the average of A, B, and C:
\[ \text{Average} = \frac{A + B + C}{3} = \frac{24 + 54 + 69}{3} \]
Calculate the sum:
\[ 24 + 54 + 69 = 147 \]
Now divide by 3:
\[ \text{Average} = \frac{147}{3} = 49 \]

### Step 7: Find the present age of D
According to the problem, the present age of D is 4 less than the average of A, B, and C:
\[ D = \text{Average} - 4 = 49 - 4 = 45 \]

### Final Answer
The present age of D is:
\[ \boxed{45} \]