The ages of Samir and Tanuj are in the ratio of 8:15. After 9years the ratio of their ages will be 11:18. what is the difference of their ages?

Options

A. a. 20years
B. b. 21years
C. c. 35years
D. d. none of these

Answer

To find the difference in ages between Samir and Tanuj, we can follow these steps:

### Step 1: Set up the initial ratio
Let the present ages of Samir and Tanuj be represented as:
- Samir's age = 8x
- Tanuj's age = 15x

Here, \( x \) is a common multiplier.

### Step 2: Set up the future ratio
After 9 years, their ages will be:
- Samir's age = \( 8x + 9 \)
- Tanuj's age = \( 15x + 9 \)

According to the problem, the ratio of their ages after 9 years will be 11:18. Thus, we can write the equation:
\[ \frac{8x + 9}{15x + 9} = \frac{11}{18} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 18(8x + 9) = 11(15x + 9) \]

### Step 4: Expand both sides
Expanding both sides results in:
\[ 144x + 162 = 165x + 99 \]

### Step 5: Rearrange the equation
Rearranging the equation to isolate \( x \):
\[ 144x - 165x = 99 - 162 \]
\[ -21x = -63 \]

### Step 6: Solve for \( x \)
Dividing both sides by -21 gives:
\[ x = 3 \]

### Step 7: Calculate the present ages
Now that we have \( x \), we can find the present ages:
- Samir's age = \( 8x = 8 \times 3 = 24 \) years
- Tanuj's age = \( 15x = 15 \times 3 = 45 \) years

### Step 8: Find the difference in ages
The difference in their ages is:
\[ \text{Difference} = \text{Tanuj's age} - \text{Samir's age} = 45 - 24 = 21 \text{ years} \]

### Final Answer
The difference in their ages is **21 years**.

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