At present mannu's age is twice the age of sannu's present age the sum of mannu's age two years hence and sannu's five years hence will be 64 years what is mannu's present age?

Options

A. 38 years
B. 34 years
C. 42 years
D. 36 years

Answer

To solve the problem step by step, we can follow these instructions:

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

### Step 2: Set Up the First Equation
According to the problem, Manu's age is twice Sannu's age. Therefore, we can write the first equation as:
\[ X = 2Y \]

### Step 3: Set Up the Second Equation
The problem states that the sum of Manu's age two years hence and Sannu's age five years hence will be 64 years. We can express this mathematically:
- Manu's age two years hence = \( X + 2 \)
- Sannu's age five years hence = \( Y + 5 \)

Thus, the second equation is:
\[ (X + 2) + (Y + 5) = 64 \]
This simplifies to:
\[ X + Y + 7 = 64 \]

### Step 4: Simplify the Second Equation
We can simplify the second equation to find a relationship between \( X \) and \( Y \):
\[ X + Y = 64 - 7 \]
\[ X + Y = 57 \]

### Step 5: Substitute the First Equation into the Second Equation
Now we can substitute \( X \) from the first equation into the second equation:
\[ 2Y + Y = 57 \]
This simplifies to:
\[ 3Y = 57 \]

### Step 6: Solve for Sannu's Age
Now, we can solve for \( Y \):
\[ Y = \frac{57}{3} \]
\[ Y = 19 \]

### Step 7: Find Manu's Present Age
Now that we have \( Y \), we can find \( X \):
\[ X = 2Y = 2 \times 19 = 38 \]

### Conclusion
Thus, Manu's present age is:
\[ \text{Manu's present age} = 38 \text{ years} \]