A water pipe is cut into two pieces. The longer piece is 70% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?

Options

A. `140%`
B. `(400)/(3)%`
C. `40%`
D. None of these

Answer

To solve the problem step by step, we will follow these calculations:

1. **Identify the lengths of the pieces**:
- Let the total length of the pipe be represented as 100% (or simply 100 units for easier calculation).
- The longer piece is 70% of the total length. Therefore, the length of the longer piece is:
\[ \text{Length of longer piece} = 70\% \text{ of } 100 = 70 \text{ units} \]

2. **Calculate the length of the shorter piece**:
- The shorter piece is the remaining part of the pipe. Since the longer piece is 70%, the shorter piece will be:
\[ \text{Length of shorter piece} = 100\% - 70\% = 30\% \text{ of } 100 = 30 \text{ units} \]

3. **Determine the difference in lengths**:
- Now, we need to find out how much longer the longer piece is compared to the shorter piece. The difference in lengths is calculated as:
\[ \text{Difference} = \text{Length of longer piece} - \text{Length of shorter piece} = 70 - 30 = 40 \text{ units} \]

4. **Calculate the percentage increase**:
- To find out by what percentage the longer piece is longer than the shorter piece, we use the formula:
\[ \text{Percentage increase} = \left( \frac{\text{Difference}}{\text{Length of shorter piece}} \right) \times 100 \]
- Substituting the values we have:
\[ \text{Percentage increase} = \left( \frac{40}{30} \right) \times 100 \]

5. **Perform the calculation**:
- Simplifying the fraction:
\[ \frac{40}{30} = \frac{4}{3} \]
- Now, multiplying by 100:
\[ \text{Percentage increase} = \frac{4}{3} \times 100 = \frac{400}{3} \approx 133.33\% \]

Thus, the longer piece is approximately \( \frac{400}{3} \% \) longer than the shorter piece.