If x:y=2:3 and 2:x=1:2 then the value of y is

Options

A. 4
B. 6
C. (1/3)
D. (3/2)

Answer

To solve the problem, we need to find the value of \( y \) given the ratios \( x:y = 2:3 \) and \( 2:x = 1:2 \).

### Step-by-Step Solution:

1. **Express the Ratios in Terms of Variables**:
From the first ratio \( x:y = 2:3 \), we can express \( x \) and \( y \) in terms of a common variable \( k \):
\[ x = 2k \quad \text{and} \quad y = 3k \]

2. **Use the Second Ratio**:
The second ratio \( 2:x = 1:2 \) can be rewritten as:
\[ \frac{2}{x} = \frac{1}{2} \]
Cross-multiplying gives:
\[ 2 \cdot 2 = 1 \cdot x \implies 4 = x \]

3. **Substitute \( x \) Back into the First Ratio**:
Now that we have \( x = 4 \), we can substitute this value back into the expression for \( x \) in terms of \( k \):
\[ 2k = 4 \implies k = 2 \]

4. **Find the Value of \( y \)**:
Now, substitute \( k \) back into the expression for \( y \):
\[ y = 3k = 3 \cdot 2 = 6 \]

5. **Conclusion**:
Therefore, the value of \( y \) is:
\[ y = 6 \]

### Final Answer:
The value of \( y \) is \( 6 \).

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