Priyamvada's present age is five years more than twice the age of his cousin Ritika. Sixteen years from now Priyamvada's age will be 150% of that of Ritika's. What is Priyamvada's present age (in years)?

Options

A. 23
B. 33
C. 17
D. 26

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given in the question.

### Step 1: Define the Variables
Let:
- Priyamvada's present age = \( X \)
- Ritika's present age = \( Y \)

### Step 2: Set Up the First Equation
According to the problem, Priyamvada's present age is five years more than twice the age of Ritika. This can be expressed as:
\[ X = 2Y + 5 \]

### Step 3: Set Up the Second Equation
The problem also states that sixteen years from now, Priyamvada's age will be 150% of Ritika's age. In 16 years, their ages will be:
- Priyamvada's age: \( X + 16 \)
- Ritika's age: \( Y + 16 \)

The relationship can be expressed as:
\[ X + 16 = 1.5 \times (Y + 16) \]

### Step 4: Simplify the Second Equation
Now, we can rewrite the second equation:
\[ X + 16 = 1.5Y + 24 \]

### Step 5: Rearrange the Second Equation
Rearranging the equation gives us:
\[ X = 1.5Y + 24 - 16 \]
\[ X = 1.5Y + 8 \]

### Step 6: Set the Two Equations Equal
Now we have two equations:
1. \( X = 2Y + 5 \)
2. \( X = 1.5Y + 8 \)

We can set these equal to each other:
\[ 2Y + 5 = 1.5Y + 8 \]

### Step 7: Solve for \( Y \)
Now, we will solve for \( Y \):
1. Subtract \( 1.5Y \) from both sides:
\[ 2Y - 1.5Y + 5 = 8 \]
\[ 0.5Y + 5 = 8 \]

2. Subtract 5 from both sides:
\[ 0.5Y = 3 \]

3. Multiply both sides by 2:
\[ Y = 6 \]

### Step 8: Find Priyamvada's Age
Now that we have \( Y \), we can find \( X \):
Using the first equation:
\[ X = 2Y + 5 \]
\[ X = 2(6) + 5 \]
\[ X = 12 + 5 \]
\[ X = 17 \]

### Conclusion
Priyamvada's present age is \( 17 \) years.