B's age is 6 years more than A. If the ratio of B's age 9 years hence to C's present age is 9:8 & the present age of C is twice of A's present age then what will be the age of B after 5 years

Options

A. 18 years
B. 25 years
C. 23 years
D. 24 years

Answer

To solve the problem step by step, let's define the variables and use the information given in the question.

### Step 1: Define the variables
Let A's present age be \( X \).
Then, B's present age will be \( X + 6 \) (since B's age is 6 years more than A's).

### Step 2: Define C's age
According to the question, C's present age is twice A's present age.
Thus, C's present age will be \( 2X \).

### Step 3: Calculate B's age 9 years hence
B's age 9 years from now will be:
\[ B's \, age \, in \, 9 \, years = (X + 6) + 9 = X + 15 \]

### Step 4: Set up the ratio
The ratio of B's age in 9 years to C's present age is given as \( 9:8 \).
This can be expressed as:
\[ \frac{B's \, age \, in \, 9 \, years}{C's \, present \, age} = \frac{9}{8} \]

Substituting the ages we have:
\[ \frac{X + 15}{2X} = \frac{9}{8} \]

### Step 5: Cross-multiply to solve for X
Cross-multiplying gives us:
\[ 8(X + 15) = 9(2X) \]
Expanding both sides:
\[ 8X + 120 = 18X \]

### Step 6: Rearranging the equation
Rearranging the equation to isolate \( X \):
\[ 120 = 18X - 8X \]
\[ 120 = 10X \]
Dividing both sides by 10:
\[ X = 12 \]

### Step 7: Find B's present age
Now that we have A's age, we can find B's present age:
\[ B's \, present \, age = X + 6 = 12 + 6 = 18 \]

### Step 8: Calculate B's age after 5 years
To find B's age after 5 years:
\[ B's \, age \, after \, 5 \, years = B's \, present \, age + 5 = 18 + 5 = 23 \]

### Final Answer
Thus, B's age after 5 years will be **23 years**.

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