A number is decreased first by 30% and then it is again decreased by 30%. What is the percentage change in the number?

Options

A. 60% decrease
B. 51% decrease
C. No change
D. 66% decrease

Answer

To solve the problem of finding the percentage change when a number is decreased first by 30% and then again by 30%, we can follow these steps:

### Step-by-Step Solution

1. **Let the Original Number be 100**:
To simplify calculations, we can assume the original number is 100.

2. **First Decrease by 30%**:
When we decrease 100 by 30%, we calculate:
\[ 100 - (30\% \text{ of } 100) = 100 - 30 = 70 \]
So, after the first decrease, the number is 70.

3. **Second Decrease by 30%**:
Now, we decrease the new number (70) by 30%:
\[ 70 - (30\% \text{ of } 70) = 70 - 21 = 49 \]
After the second decrease, the number is 49.

4. **Calculate the Total Decrease**:
The original number was 100, and now we have 49. The total decrease is:
\[ 100 - 49 = 51 \]

5. **Calculate the Percentage Change**:
To find the percentage change, we use the formula:
\[ \text{Percentage Change} = \left(\frac{\text{Decrease}}{\text{Original Number}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left(\frac{51}{100}\right) \times 100 = 51\% \]

### Conclusion
The percentage change in the number after two successive decreases of 30% each is **51%**.

---