Vishal is 20 years younger to Arya. Twelve years hence Arya's age will be 1.25 times that of Vishal. Arya is now __ years old.

Options

A. 78
B. 68
C. 88
D. 72

Answer

To solve the problem step by step, we will define the ages of Vishal and Arya based on the information provided.

### Step 1: Define Variables
Let the present age of Vishal be \( V \) years. Since Vishal is 20 years younger than Arya, Arya's present age can be expressed as:
\[ A = V + 20 \]

### Step 2: Age After 12 Years
In 12 years, Vishal's age will be:
\[ V + 12 \]
And Arya's age will be:
\[ A + 12 = (V + 20) + 12 = V + 32 \]

### Step 3: Set Up the Equation
According to the problem, in 12 years, Arya's age will be 1.25 times Vishal's age. Therefore, we can set up the equation:
\[ V + 32 = 1.25 \times (V + 12) \]

### Step 4: Expand and Simplify the Equation
Expanding the right side of the equation gives:
\[ V + 32 = 1.25V + 15 \]
Now, we will rearrange the equation to isolate \( V \):
\[ V + 32 - 15 = 1.25V \]
\[ 17 = 1.25V - V \]
\[ 17 = 0.25V \]

### Step 5: Solve for Vishal's Age
To find \( V \), divide both sides by 0.25:
\[ V = \frac{17}{0.25} = 68 \]

### Step 6: Calculate Arya's Age
Now that we have Vishal's age, we can find Arya's age:
\[ A = V + 20 = 68 + 20 = 88 \]

### Conclusion
Arya's present age is:
\[ \boxed{88} \text{ years} \]