A computer typist types a page with 20 lines in 10 minutes but he lives `8%` margin on the left side of the page. Now he has to type 23 pages with 40 lines on each page which he leves `25%` more margin than before. How much time is now required to type these 23 pages?

Options

A. `7 1/2` hrs
B. `8 1/2`hrs
C. `23 1/2` hrs
D. 3916 hrs

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Determine the effective lines typed per minute
The typist types 20 lines in 10 minutes. Therefore, the number of lines typed per minute is:
\[ \text{Lines per minute} = \frac{20 \text{ lines}}{10 \text{ minutes}} = 2 \text{ lines per minute} \]

**Hint:** To find the rate of work, divide the total work done by the time taken.

### Step 2: Calculate the effective lines typed considering the margin
The typist leaves an 8% margin on the page. This means he effectively types 92% of the lines on the page. For a page with 20 lines:
\[ \text{Effective lines per page} = 20 \text{ lines} \times 92\% = 20 \times 0.92 = 18.4 \text{ lines} \]
Since we can't have a fraction of a line, we can round this to 18 lines for practical purposes.

**Hint:** To find the effective work done, multiply the total work by the percentage of work completed.

### Step 3: Calculate the new margin
Now, the typist has to type 23 pages with 40 lines each, but he leaves 25% more margin than before. The original margin was 8%, so:
\[ \text{New margin} = 8\% + 25\% \text{ of } 8\% = 8\% + 2\% = 10\% \]
Thus, the effective lines typed on each page with the new margin becomes:
\[ \text{Effective lines per page} = 40 \text{ lines} \times (100\% - 10\%) = 40 \times 0.90 = 36 \text{ lines} \]

**Hint:** To find the new margin, calculate the percentage increase and add it to the original margin.

### Step 4: Calculate the total lines to be typed
Now, the total number of lines to be typed for 23 pages is:
\[ \text{Total lines} = 23 \text{ pages} \times 36 \text{ lines per page} = 828 \text{ lines} \]

**Hint:** To find the total work, multiply the number of pages by the number of lines per page.

### Step 5: Calculate the total time required
Since the typist types 2 lines per minute, the time required to type 828 lines is:
\[ \text{Time (in minutes)} = \frac{828 \text{ lines}}{2 \text{ lines per minute}} = 414 \text{ minutes} \]

**Hint:** To find the time required, divide the total work by the rate of work.

### Step 6: Convert minutes to hours
To convert the time from minutes to hours:
\[ \text{Time (in hours)} = \frac{414 \text{ minutes}}{60} = 6.9 \text{ hours} \approx 6 \text{ hours and } 54 \text{ minutes} \]

**Hint:** To convert minutes to hours, divide by 60.

### Final Answer
The total time required to type the 23 pages is approximately 6 hours and 54 minutes.

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