A water pipe is cut into two pieces- The longer piece is 64% of the length of the pipe- By how much percentage is the longer piece longer than the shorter piece ?

Options

A. `77.77%`
B. `81.81%`
C. 0.36
D. None of these

Answer

To solve the problem step by step, we need to find out how much percentage the longer piece is longer than the shorter piece after cutting the water pipe.

### Step 1: Define the total length of the pipe
Let the total length of the pipe be represented as 100 units (this makes calculations easier as we can directly use percentages).

### Step 2: Calculate the length of the longer piece
The longer piece is given as 64% of the total length of the pipe. Therefore, the length of the longer piece is:
\[ \text{Length of longer piece} = 64\% \text{ of } 100 = 64 \text{ units} \]

### Step 3: Calculate the length of the shorter piece
Since the total length of the pipe is 100 units, the length of the shorter piece can be calculated as:
\[ \text{Length of shorter piece} = 100\% - 64\% = 36\% \text{ of } 100 = 36 \text{ units} \]

### Step 4: Calculate the difference in length between the two pieces
Now, we find the difference in length between the longer piece and the shorter piece:
\[ \text{Difference in length} = \text{Length of longer piece} - \text{Length of shorter piece} = 64 - 36 = 28 \text{ units} \]

### Step 5: Calculate the percentage by which the longer piece is longer than the shorter piece
To find out by what percentage the longer piece is longer than the shorter piece, we use the formula:
\[ \text{Percentage increase} = \left( \frac{\text{Difference in length}}{\text{Length of shorter piece}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage increase} = \left( \frac{28}{36} \right) \times 100 \]

### Step 6: Calculate the final percentage
Now we perform the calculation:
\[ \text{Percentage increase} = \left( \frac{28}{36} \right) \times 100 = \frac{2800}{36} \approx 77.78\% \]

### Conclusion
Thus, the longer piece is approximately **77.78%** longer than the shorter piece.

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