Find the number which when decreased by `15%` becomes 680.

Answer

To solve the problem step by step, we need to find the number (let's call it \( x \)) that, when decreased by 15%, results in 680.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find a number \( x \) such that when we decrease it by 15%, we get 680.

2. **Setting Up the Equation**:
When we decrease \( x \) by 15%, we can express this mathematically as:
\[ x - 15\% \text{ of } x = 680 \]
We can express 15% as a decimal:
\[ 15\% = \frac{15}{100} = 0.15 \]
Therefore, the equation becomes:
\[ x - 0.15x = 680 \]

3. **Simplifying the Equation**:
Combine like terms on the left side:
\[ (1 - 0.15)x = 680 \]
This simplifies to:
\[ 0.85x = 680 \]

4. **Solving for \( x \)**:
To find \( x \), divide both sides of the equation by 0.85:
\[ x = \frac{680}{0.85} \]

5. **Calculating the Value**:
Now, perform the division:
\[ x = 800 \]

6. **Conclusion**:
The number which, when decreased by 15%, becomes 680 is \( \boxed{800} \).