Sneh's age is `1/6` th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before then what is Sneh's present age?

Options

A. `6 2/3` years
B. 24 years
C. 30 years
D. 5 years

Answer

To solve the problem step by step, we will define the variables and use the information given in the question.

### Step 1: Define Variables
Let S be Sneh's current age and F be her father's current age.

### Step 2: Establish Relationships
From the problem, we know:
1. Sneh's age is \( \frac{1}{6} \) of her father's age.
\[ S = \frac{1}{6}F \quad \text{or} \quad F = 6S \]

### Step 3: Analyze Vimal's Age
The problem states that Vimal's 8th birthday was celebrated 2 years ago. Therefore, Vimal's current age is:
\[ 8 + 2 = 10 \text{ years} \]

### Step 4: Future Age Relationships
According to the problem, Sneh's father's age will be twice Vimal's age after 10 years. In 10 years, Vimal's age will be:
\[ 10 + 10 = 20 \text{ years} \]
Thus, Sneh's father's age in 10 years will be:
\[ F + 10 \]
Setting this equal to twice Vimal's age in 10 years gives us:
\[ F + 10 = 2 \times 20 \]
\[ F + 10 = 40 \]

### Step 5: Solve for Father's Age
Now, we can solve for F:
\[ F = 40 - 10 = 30 \]

### Step 6: Calculate Sneh's Age
Using the relationship \( F = 6S \):
\[ 30 = 6S \]
Dividing both sides by 6 gives:
\[ S = \frac{30}{6} = 5 \]

### Conclusion
Sneh's present age is \( \boxed{5} \) years.

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