The ratio of age of A and B is 8:9 and the age of B is 2/3 of C's age and age of C is `9/13` times the age of D. If the age of B is 18 years then the age of C is

Options

A. 36 years
B. 39 years
C. 27 years
D. 54 years

Answer

To solve the problem step by step, we will use the information provided about the ages of A, B, C, and D.

### Step 1: Understand the ratio of ages
The ratio of the ages of A and B is given as 8:9. This means that if we let the age of A be \( 8x \) and the age of B be \( 9x \), where \( x \) is a common multiplier.

### Step 2: Find the value of \( x \)
We know that the age of B is given as 18 years. Therefore, we can set up the equation:
\[ 9x = 18 \]
To find \( x \), we divide both sides by 9:
\[ x = \frac{18}{9} = 2 \]

### Step 3: Calculate the age of A
Now that we have \( x \), we can find the age of A:
\[ \text{Age of A} = 8x = 8 \times 2 = 16 \text{ years} \]

### Step 4: Relate the age of B to C
According to the problem, the age of B is \( \frac{2}{3} \) of C's age. We can express this as:
\[ B = \frac{2}{3}C \]
Substituting the age of B (which is 18 years):
\[ 18 = \frac{2}{3}C \]

### Step 5: Solve for C's age
To find C's age, we can rearrange the equation:
\[ C = 18 \times \frac{3}{2} \]
Calculating this gives:
\[ C = 18 \times 1.5 = 27 \text{ years} \]

### Step 6: Conclusion
Thus, the age of C is 27 years.