The ratio of present ages of A and B is 8 : 9. After 9 years, the ratio will become 19 : 21. C is 3 years younger to B. What is the present age (In years) of C ?
A और B की वर्तमान आयु का अनुपात 8 : 9 है | 9 वर्ष के बाद, यह अनुपात 19 : 21 हो जाएगा | C, B से 3 वर्ष छोटा है | C की वर्तमान उम्र (वर्ष में ) कितनी है ?

Options

A. 49
B. 48
C. 51
D. 52

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the present ages of A and B
Let the present ages of A and B be represented as:
- Age of A = 8x
- Age of B = 9x

### Step 2: Set up the equation for their ages after 9 years
After 9 years, the ages of A and B will be:
- Age of A after 9 years = 8x + 9
- Age of B after 9 years = 9x + 9

According to the problem, the ratio of their ages after 9 years will be 19:21. Therefore, we can set up the equation:
\[ \frac{8x + 9}{9x + 9} = \frac{19}{21} \]

### Step 3: Cross multiply to eliminate the fraction
Cross multiplying gives us:
\[ 21(8x + 9) = 19(9x + 9) \]

### Step 4: Expand both sides
Expanding both sides, we get:
\[ 168x + 189 = 171x + 171 \]

### Step 5: Rearrange the equation to isolate x
Now, we will move all terms involving x to one side and constant terms to the other side:
\[ 168x - 171x = 171 - 189 \]
This simplifies to:
\[ -3x = -18 \]

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

### Step 7: Find the present age of B
Now that we have the value of x, we can find the present age of B:
\[ \text{Age of B} = 9x = 9 \times 6 = 54 \text{ years} \]

### Step 8: Find the present age of C
Since C is 3 years younger than B, we can find C's age as follows:
\[ \text{Age of C} = 54 - 3 = 51 \text{ years} \]

### Final Answer
The present age of C is **51 years**.

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