A man can write 20 lines in 10 minutes but he left `8%` of the space blank in a line. Find the time required to write 23 pages of 40 lines, If now he leaves `25%` more blank space than before ?

Options

A. `380` min
B. `450` min
C. `361` min
D. `375` min

Answer

To solve the problem, we need to follow these steps:

### Step 1: Determine the number of lines to be written
The question states that there are 23 pages with 40 lines each.

\[ \text{Total lines} = \text{Number of pages} \times \text{Lines per page} = 23 \times 40 = 920 \text{ lines} \]

### Step 2: Calculate the effective lines written by the man
Initially, the man writes 20 lines in 10 minutes but leaves 8% of the space blank in each line. This means he effectively writes 92% of each line.

\[ \text{Effective lines written} = 20 \times (1 - 0.08) = 20 \times 0.92 = 18.4 \text{ lines in 10 minutes} \]

### Step 3: Determine the new percentage of blank space
The problem states that he now leaves 25% more blank space than before.

\[ \text{New blank space percentage} = 8\% + 25\% \text{ of } 8\% = 8\% + 2\% = 10\% \]

### Step 4: Calculate the new effective lines written
Now, with 10% of the space blank, the effective lines he writes are:

\[ \text{Effective lines written} = 20 \times (1 - 0.10) = 20 \times 0.90 = 18 \text{ lines in 10 minutes} \]

### Step 5: Calculate the total time required to write 920 lines
To find the total time required to write 920 lines at the new effective rate:

\[ \text{Time required} = \frac{\text{Total lines}}{\text{Effective lines per 10 minutes}} \times 10 \text{ minutes} \]

\[ \text{Time required} = \frac{920}{18} \times 10 \approx 511.11 \text{ minutes} \]

### Step 6: Round the time to a practical value
Since time is usually rounded to the nearest whole number, we can say:

\[ \text{Total time required} \approx 511 \text{ minutes} \]

### Final Answer
The time required to write 23 pages of 40 lines, leaving 25% more blank space than before, is approximately **511 minutes**.

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