Deepak is twice as old as Vikas was 3 year ago when Deepak was old as Vikas today. if the difference between their ages today be five year what is the present age of Deepak?

Options

A. 12 years
B. 16 years
C. 18 years
D. 14 years

Answer

To solve the problem, let's define the current ages of Deepak and Vikas.

Let:
- D = Current age of Deepak
- V = Current age of Vikas

According to the problem, we have the following information:

1. The difference between their ages today is 5 years:
\[ D - V = 5 \quad \text{(Equation 1)} \]

2. Deepak is twice as old as Vikas was 3 years ago when Deepak was as old as Vikas is today.

To express this mathematically, we need to determine Vikas's age 3 years ago:
\[ \text{Vikas's age 3 years ago} = V - 3 \]

At that time, Deepak's age was:
\[ D - 3 \]

According to the problem, when Deepak was as old as Vikas is today (which is V), we have:
\[ D - 3 = V \]

Now, substituting this into the first condition, we can express Deepak's age in terms of Vikas's age:
\[ D = V + 3 \quad \text{(Equation 2)} \]

3. Now we can substitute Equation 2 into Equation 1:
\[ (V + 3) - V = 5 \]
Simplifying this gives:
\[ 3 = 5 \]
This is incorrect, indicating that we need to correctly interpret the relationships.

Let's correctly analyze the second condition:
Deepak is twice as old as Vikas was 3 years ago when Deepak was as old as Vikas is today.

Using the information:
- When Deepak was V years old (which is Vikas's current age), that was 3 years ago:
\[ D - 3 = V \quad \Rightarrow \quad D = V + 3 \]

Now, substituting this into the first equation:
\[ D - V = 5 \quad \Rightarrow \quad (V + 3) - V = 5 \]
This simplifies to:
\[ 3 = 5 \]
This indicates a misinterpretation of the conditions.

Let's analyze the conditions again:
1. Deepak is twice as old as Vikas was 3 years ago:
\[ D = 2(V - 3) \]

2. We already have:
\[ D - V = 5 \quad \text{(Equation 1)} \]

Now, substituting \(D\) from the first equation into the second:
\[ 2(V - 3) - V = 5 \]
Expanding this gives:
\[ 2V - 6 - V = 5 \]
Simplifying leads to:
\[ V - 6 = 5 \]
Thus:
\[ V = 11 \]

Now substituting \(V\) back into Equation 2 to find \(D\):
\[ D = V + 3 = 11 + 3 = 14 \]

Therefore, the present age of Deepak is:
\[ \boxed{14} \]