If `3:21::x:63`,find the value of x. (i) '8' (ii) '9' (iii) '7' (iv) '3'

Answer

To solve the proportion \(3:21::x:63\), we can set up the equation based on the property of ratios:

1. **Set up the equation**:
\[ \frac{3}{21} = \frac{x}{63} \]

2. **Cross-multiply**:
\[ 3 \times 63 = 21 \times x \]
This simplifies to:
\[ 189 = 21x \]

3. **Solve for \(x\)**:
To isolate \(x\), divide both sides by 21:
\[ x = \frac{189}{21} \]

4. **Calculate the value**:
Now, perform the division:
\[ x = 9 \]

Thus, the value of \(x\) is \(9\).

### Final Answer:
The value of \(x\) is \(9\), which corresponds to option (ii).