A woman reduces her weight in the ratio `7 : 5`. What does her weight become if originally it was 84 kg?

Answer

To solve the problem step by step, we will follow the given information about the weight reduction in the ratio of 7:5.

### Step-by-Step Solution:

1. **Identify the Original Weight**:
The original weight of the woman is given as 84 kg.

2. **Understand the Ratio**:
The woman reduces her weight in the ratio of 7:5. This means that for every 7 parts of her original weight, she now has 5 parts of her reduced weight.

3. **Set Up the Ratio**:
We can express the relationship between the original weight and the reduced weight using the ratio:
\[ \frac{\text{Original Weight}}{\text{Reduced Weight}} = \frac{7}{5} \]
Let the reduced weight be \( x \) kg. Therefore, we can write:
\[ \frac{84}{x} = \frac{7}{5} \]

4. **Cross Multiply**:
To solve for \( x \), we can cross-multiply:
\[ 84 \times 5 = 7 \times x \]
This simplifies to:
\[ 420 = 7x \]

5. **Solve for \( x \)**:
Now, divide both sides by 7 to find \( x \):
\[ x = \frac{420}{7} = 60 \]

6. **Conclusion**:
The reduced weight of the woman is 60 kg.

### Final Answer:
The woman's weight after reduction becomes **60 kg**.

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