Age of X is six times that of Y. After 4 years , X is four times elder to Y. What is the present age of Y ?

Options

A. 4 years
B. 5 years
C. 6 years
D. 7years

Explanation

To solve the problem step by step, let's denote the present age of Y as \( y \). According to the problem, we have the following information:

1. The age of X is six times that of Y.
2. After 4 years, X is four times elder than Y.

### Step 1: Set up the equations based on the information given.

From the first statement, we can express the age of X in terms of Y:
\[ x = 6y \]

### Step 2: Write the equation for their ages after 4 years.

After 4 years, the age of X will be:
\[ x + 4 = 6y + 4 \]
The age of Y after 4 years will be:
\[ y + 4 \]

### Step 3: Set up the equation based on the second statement.

According to the second statement, after 4 years, X is four times elder than Y. This means:
\[ 6y + 4 = 4(y + 4) \]

### Step 4: Expand and simplify the equation.

Expanding the right side:
\[ 6y + 4 = 4y + 16 \]

Now, let's isolate \( y \):
\[ 6y + 4 - 4y = 16 \]
\[ 2y + 4 = 16 \]

### Step 5: Solve for \( y \).

Subtract 4 from both sides:
\[ 2y = 12 \]
Now divide by 2:
\[ y = 6 \]

### Conclusion: Present age of Y.

The present age of Y is:
\[ \boxed{6} \]