The age of X is `(2)/(3)` rd that of Y. After 6 years X will be 46 years old. The present age of Y is

Options

A. 40 years
B. 56 years
C. 60 years
D. 100 years

Explanation

To find the present age of Y, we can follow these steps:

### Step 1: Define the variables
Let the present age of X be \( X \) and the present age of Y be \( Y \).

### Step 2: Set up the equations
According to the problem, the age of X is \(\frac{2}{3}\) of the age of Y. This gives us our first equation:
\[ X = \frac{2}{3}Y \quad \text{(Equation 1)} \]

### Step 3: Use the information about future age
We know that after 6 years, X will be 46 years old. Therefore, we can express this as:
\[ X + 6 = 46 \]

### Step 4: Solve for X
From the equation \(X + 6 = 46\), we can isolate \(X\):
\[ X = 46 - 6 \]
\[ X = 40 \]

### Step 5: Substitute X into Equation 1
Now that we have the present age of X, we can substitute \(X = 40\) into Equation 1:
\[ 40 = \frac{2}{3}Y \]

### Step 6: Solve for Y
To find \(Y\), we can rearrange the equation:
\[ Y = \frac{3}{2} \times 40 \]
\[ Y = \frac{120}{2} \]
\[ Y = 60 \]

### Conclusion
The present age of Y is \(60\) years.

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