Amit is five years older than Vaibhav at present. After four years the ratio of their age will be 5:4. What is Amit age (in year) at present?

Options

A. 12
B. 16
C. 18
D. 21

Answer

To solve the problem step by step, let's define the ages of Amit and Vaibhav.

### Step 1: Define Variables
Let Vaibhav's current age be \( V \) years. Since Amit is 5 years older than Vaibhav, we can express Amit's age as:
\[ A = V + 5 \]

### Step 2: Set Up the Future Age Equation
In 4 years, Vaibhav's age will be \( V + 4 \) and Amit's age will be \( A + 4 \). According to the problem, the ratio of their ages after 4 years will be 5:4. We can set up the equation:
\[ \frac{A + 4}{V + 4} = \frac{5}{4} \]

### Step 3: Cross Multiply to Eliminate the Fraction
Cross multiplying gives us:
\[ 4(A + 4) = 5(V + 4) \]

### Step 4: Substitute Amit's Age
Now we substitute \( A \) with \( V + 5 \):
\[ 4((V + 5) + 4) = 5(V + 4) \]
This simplifies to:
\[ 4(V + 9) = 5(V + 4) \]

### Step 5: Expand Both Sides
Expanding both sides, we get:
\[ 4V + 36 = 5V + 20 \]

### Step 6: Rearrange the Equation
Now, rearranging the equation to isolate \( V \):
\[ 36 - 20 = 5V - 4V \]
\[ 16 = V \]

### Step 7: Find Amit's Age
Now that we have Vaibhav's age, we can find Amit's age:
\[ A = V + 5 = 16 + 5 = 21 \]

### Conclusion
Thus, Amit's current age is:
\[ \boxed{21} \text{ years} \]

---