Question

A computer typist types a page with 20 lines in 10 minutes but he leaves 8 percent margin on the left side of the page. Now he has to type 23 pages with 40 lines on each page which leaves 25 percent more margin than before. How much time is now required to type these 23 pages.
\[
  {\text{A}}{\text{. 7}}\dfrac{1}{2}{\text{ hrs}} \\
  {\text{B}}{\text{. 7}}\dfrac{2}{3}{\text{ hrs}} \\
  {\text{C}}{\text{. 23}}\dfrac{1}{2}{\text{ hrs}} \\
  {\text{D}}{\text{. 3}}{\text{.916 hrs}} \\
\]

Answer 1

Hint: In order to deal with this problem first, we assume that each line has 100 characters with a margin of 8 percent in order to determine the total time needed to type 23 pages, we must add the total number of characters and the time required to type one.

Complete step by step answer:
Given statement is a computer typist types a page with 20 lines in 10 minutes but he leaves 8 percent margin on the left side of the page. Now he has to type 23 pages with 40 lines on each page which leaves 25 percent more margin than before.
Let every line have 100 characters with an 8 percent margin.
The total number of characters written in one line = 100-8 = 92
Time taken to write 20 lines = 10 minutes
Time taken to write 1 character = $\dfrac{{10}}{{92 \times 20}}$ minutes
Now when the margin is increased by 25 percent, we get
New margin = $8 + 0.25 \times 8 = 10$
So number of character per line is 90
Total number of character to be written = Number of characters per line $ \times $ Number of lines per page $ \times $ Number of pages
$ \Rightarrow $ Total number of character to be written = $90 \times 40 \times 23$
Total time taken to type 23 pages = Total number of characters × Time required to type 1 character
$ \Rightarrow $ Total time taken to type 23 pages = $90 \times 40 \times 23 \times \dfrac{{10}}{{92 \times 20}} = 450$ minutes
Now we will convert the time obtained in minutes into hours by dividing it with 60, we get
$ \Rightarrow $ Total time taken to type 23 pages = $\dfrac{{450}}{{60}} = \dfrac{{15}}{2} = 7\dfrac{1}{2}$ hours
Hence the required answer is option A.
Note:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. In this particular problem, we have assumed that there are 100 characters in a line just for ease. Also, we have converted the final answer in terms of mixed fraction. Any mixed fraction can be given as ${\text{a}}\dfrac{{\text{b}}}{{\text{c}}} = \left( {{\text{a}} \times {\text{c}}} \right) + {\text{b}}$.