The ratio of Varun's age and his mother's age is 5:11. The difference is 18 years. The ratio of their ages after 5 years will be:

Options

A. 0.83263888888889
B. 0.085416666666667
C. 37:75
D. 0.42986111111111

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the Ages Based on the Given Ratio
Let Varun's age be represented as \(5x\) and his mother's age as \(11x\), where \(x\) is a common multiplier.

### Step 2: Set Up the Equation for the Age Difference
According to the problem, the difference between their ages is 18 years. Therefore, we can set up the equation:
\[ 11x - 5x = 18 \]

### Step 3: Solve for \(x\)
Simplifying the equation gives:
\[ 6x = 18 \]
Now, divide both sides by 6:
\[ x = 3 \]

### Step 4: Calculate Their Current Ages
Now that we have \(x\), we can find their current ages:
- Varun's age:
\[ 5x = 5 \times 3 = 15 \text{ years} \]
- Mother's age:
\[ 11x = 11 \times 3 = 33 \text{ years} \]

### Step 5: Calculate Their Ages After 5 Years
After 5 years, their ages will be:
- Varun's age:
\[ 15 + 5 = 20 \text{ years} \]
- Mother's age:
\[ 33 + 5 = 38 \text{ years} \]

### Step 6: Find the Ratio of Their Ages After 5 Years
Now we can find the ratio of their ages after 5 years:
\[ \text{Ratio} = \frac{20}{38} \]
To simplify this, we can divide both numbers by 2:
\[ \frac{20 \div 2}{38 \div 2} = \frac{10}{19} \]

### Final Answer
The ratio of Varun's age to his mother's age after 5 years will be \(10:19\).

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