Reena weighed 63 kg. She reduced her weight in the ratio 9 : 8 . Find her new weight .

Answer

To find Reena's new weight after reducing it in the ratio of 9:8, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio of Reena's present weight to her new weight is given as 9:8. This means that for every 9 parts of her original weight, her new weight is 8 parts.

2. **Set Up the Equation**: Let Reena's new weight be represented by \( x \). According to the ratio, we can express this relationship as:
\[ \frac{\text{Present Weight}}{\text{New Weight}} = \frac{9}{8} \]
Substituting her present weight (63 kg) into the equation, we have:
\[ \frac{63}{x} = \frac{9}{8} \]

3. **Cross Multiply**: To eliminate the fraction, we can cross multiply:
\[ 63 \times 8 = 9 \times x \]
This simplifies to:
\[ 504 = 9x \]

4. **Solve for \( x \)**: To find \( x \), divide both sides of the equation by 9:
\[ x = \frac{504}{9} \]

5. **Calculate the Value**: Now, perform the division:
\[ x = 56 \]

6. **Conclusion**: Therefore, Reena's new weight after the reduction is **56 kg**.