If $$x$$ and $$y$$ vary inversely to each other, and $$x = 7$$ when $$y = 12$$, find $$y$$ when $$x = 21$$.

Question

Accepted Answer

1. **Understand the inverse variation formula**:  
   When $$x$$ and $$y$$ vary inversely, the product of $$x$$ and $$y$$ remains constant:  
   $$
   x_1 \cdot y_1 = x_2 \cdot y_2
   $$

2. **Substitute the given values**:  
   - $$x_1 = 7$$, $$y_1 = 12$$, and $$x_2 = 21$$.  
   Using the formula:  
   $$
   7 \cdot 12 = 21 \cdot y
   $$

3. **Solve for $$y$$**:  
   Simplify:  
   $$
   y = \frac{7 \cdot 12}{21} = \frac{84}{21} = 4
   $$

Thus, when $$x = 21$$, $$y = 4$$. The correct answer is **(b) 4**.

Answer

Answer

Answer