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 Arya and Vishal, set up the equations based on the information given, and then solve for Arya's current age.

### Step 1: Define the variables
Let Arya's current age be \( X \). Since Vishal is 20 years younger than Arya, Vishal's current age will be \( X - 20 \).

**Hint:** Define the ages of the individuals based on the relationships given in the problem.

### Step 2: Determine their ages in 12 years
In 12 years, Arya's age will be \( X + 12 \) and Vishal's age will be \( (X - 20) + 12 = X - 8 \).

**Hint:** Remember to add 12 years to both ages to find their ages in the future.

### Step 3: Set up the equation based on the problem statement
According to the problem, in 12 years, Arya's age will be 1.25 times Vishal's age. This gives us the equation:
\[ X + 12 = 1.25 \times (X - 8) \]

**Hint:** Translate the verbal statement into a mathematical equation.

### Step 4: Solve the equation
Now, we will solve the equation:
\[ X + 12 = 1.25(X - 8) \]
Expanding the right side:
\[ X + 12 = 1.25X - 10 \]
Now, rearranging the equation:
\[ X - 1.25X = -10 - 12 \]
\[ -0.25X = -22 \]
Dividing both sides by -0.25:
\[ X = \frac{22}{0.25} = 88 \]

**Hint:** Isolate the variable to find its value.

### Step 5: Conclusion
Arya's current age is \( 88 \) years.

**Final Answer:** Arya is now 88 years old.