The ratio of ages of jai is `5:2`. The sum of their ages is 63. After 9 years what will be the ratio of their ages ?
A. `5:2`
B. `2:1`
C. `3:2`
D. `4:3`

Options

A. C
B. B
C. A
D. D

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the ages based on the ratio
Let the age of Jai be represented as \(5x\) and the age of the other person be represented as \(2x\).

### Step 2: Set up the equation for the sum of ages
According to the problem, the sum of their ages is 63. Therefore, we can write the equation:
\[ 5x + 2x = 63 \]

### Step 3: Simplify the equation
Combine the terms on the left side:
\[ 7x = 63 \]

### Step 4: Solve for \(x\)
To find \(x\), divide both sides of the equation by 7:
\[ x = \frac{63}{7} = 9 \]

### Step 5: Calculate the present ages
Now that we have \(x\), we can find the present ages:
- Jai's age: \(5x = 5 \times 9 = 45\)
- Other person's age: \(2x = 2 \times 9 = 18\)

### Step 6: Calculate their ages after 9 years
After 9 years, Jai's age will be:
\[ 45 + 9 = 54 \]
And the other person's age will be:
\[ 18 + 9 = 27 \]

### Step 7: Find the ratio of their ages after 9 years
Now, we need to find the ratio of their ages after 9 years:
\[ \text{Ratio} = \frac{54}{27} = 2 \]
Thus, the ratio can be expressed as:
\[ 2:1 \]

### Conclusion
The ratio of their ages after 9 years will be \(2:1\).

### Final Answer
The correct option is **B. \(2:1\)**.

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