A report consists of 20 sheets of 56 lines and such line consists of 65 characters. The report is reduced into sheets, each of 65 lines such that each line consists of 70 characters. What is the percentage reduction in the number of sheets ?

Answer

To solve the problem step by step, we will calculate the total number of characters in the original report and the new report, and then determine the percentage reduction in the number of sheets.

### Step 1: Calculate the total number of characters in the original report.
- The original report consists of 20 sheets.
- Each sheet has 56 lines.
- Each line has 65 characters.

**Total characters in the original report:**
\[ \text{Total characters} = \text{Number of sheets} \times \text{Number of lines per sheet} \times \text{Number of characters per line} \]
\[ \text{Total characters} = 20 \times 56 \times 65 \]

### Step 2: Calculate the total number of characters in the new report.
- The new report consists of sheets with 65 lines each.
- Each line has 70 characters.

**Total characters in the new report:**
\[ \text{Total characters} = x \times 65 \times 70 \]
Where \( x \) is the new number of sheets.

### Step 3: Set the total characters in both reports equal to each other.
Since the total number of characters remains the same:
\[ 20 \times 56 \times 65 = x \times 65 \times 70 \]

### Step 4: Simplify the equation.
We can cancel out 65 from both sides:
\[ 20 \times 56 = x \times 70 \]

### Step 5: Solve for \( x \).
\[ x = \frac{20 \times 56}{70} \]
Calculating \( 20 \times 56 = 1120 \):
\[ x = \frac{1120}{70} = 16 \]

### Step 6: Calculate the percentage reduction in the number of sheets.
- Original number of sheets = 20
- New number of sheets = 16

**Percentage reduction:**
\[ \text{Percentage reduction} = \frac{\text{Original sheets} - \text{New sheets}}{\text{Original sheets}} \times 100 \]
\[ \text{Percentage reduction} = \frac{20 - 16}{20} \times 100 = \frac{4}{20} \times 100 = 20\% \]

### Final Answer:
The percentage reduction in the number of sheets is **20%**.