Sunil's age is `1/6` of Neelam's age . After 10 years, Neelam's age will be twice the Priya's age. If 2 years ago, Priya was 8 years old, what will be Sunil's age after 5 years?

Options

A. 5 years
B. 8 years
C. 12 years
D. 10 years

Answer

To solve the problem step by step, we will define the ages of Sunil, Neelam, and Priya using algebra.

### Step 1: Define the variables
Let Neelam's current age be \( N \). According to the problem, Sunil's age is \( \frac{1}{6} \) of Neelam's age. Therefore, we can express Sunil's age as:
\[ S = \frac{1}{6} N \]

### Step 2: Determine Priya's current age
The problem states that 2 years ago, Priya was 8 years old. Therefore, her current age is:
\[ P = 8 + 2 = 10 \]

### Step 3: Set up the equation for ages after 10 years
After 10 years, Neelam's age will be:
\[ N + 10 \]
And Priya's age will be:
\[ P + 10 = 10 + 10 = 20 \]

According to the problem, after 10 years, Neelam's age will be twice Priya's age:
\[ N + 10 = 2(P + 10) \]
Substituting Priya's current age into the equation gives us:
\[ N + 10 = 2 \times 20 \]
\[ N + 10 = 40 \]

### Step 4: Solve for Neelam's age
Now, we can solve for Neelam's age:
\[ N = 40 - 10 \]
\[ N = 30 \]

### Step 5: Calculate Sunil's current age
Now that we know Neelam's age, we can find Sunil's age:
\[ S = \frac{1}{6} N = \frac{1}{6} \times 30 = 5 \]

### Step 6: Determine Sunil's age after 5 years
To find Sunil's age after 5 years, we add 5 to his current age:
\[ S + 5 = 5 + 5 = 10 \]

### Final Answer
Sunil's age after 5 years will be **10 years**.

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