Question

A computer typist types a page with $20$ lines in $10$ minutes but he leaves $8\% $ margin on the left side of the page. Now he has to type \[23\] pages with the \[40\] line on each page which leaves \[25\% \] more margin than before. How much time is now required to type these \[23\] pages.
(a) \[7{\text{ }}\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/
 \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ }}hrs\]
(b) \[7{\text{ }}2/3{\text{ }}hrs\]
(c) \[23{\text{ }}\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/
 \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ }}hrs\]
(d) \[3.916{\text{ }}hrs\]

Answer 1

Hint- In order to deal with this problem first, we assume that each line has $100$ characters with a margin of $8\% $ 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 solution -
Given statement is a computer typist types a page with $20$ lines in $10$ minutes but he leaves $8\% $margin on the left side of the page. Now he has to type \[23\] pages with the \[40\] line on each page which leaves \[25\% \] more margin than before.
Let every line have $100$ characters with $8\% $ margin.
The total number of characters written in one line = \[100 - 8 = 92 \]
Time taken to write $20$ lines is $10$ minutes
So time taken to write $1$ line with \[92\] characters = \[10/(92 \times 20)\]
Now when the margin is increased by \[25\% \]
 = New margin is
\[ = 8 + \dfrac{{25}}{{100}} \times 8 \\
   = 8 + \dfrac{1}{4} \times 8 \\
   = 8 + 2 \\
   = 10 \\ \]
So number of character per line is \[90\]
Total number of character to be written = $90 \times 23 = 2070 $
Number of characters per line × number of lines per page × number of pages
\[90{\text{ }} \times {\text{ }}40{\text{ }} \times {\text{ }}23\]
Total time taken to type 23 pages = Total number of characters $ \times $ Time required to type one character.
\[ = (90{\text{ }} \times {\text{ }}40{\text{ }} \times {\text{ }}23) \times \dfrac{{10}}{{92 \times 20}} \\
   = (3600 \times 23) \times \dfrac{1}{{92 \times 2}} \\
   = 82,800 \times \dfrac{1}{{92 \times 2}} \\
   = 82,800 \times \dfrac{1}{{184}} \\
   = 450{\text{ minutes}} \\ \]
Now we will convert obtained minutes in hours by dividing it with \[60\]
\[\dfrac{{450}}{{60}}{\text{ }} = {\text{ }}7\dfrac{1}{2}\]
Hence the required answer is option A.

Note- In mathematics, a percentage is a number or ratio expressed as a fraction of $100$. The top number (the numerator) says how many parts we have. The bottom number (the denominator) says how many equal parts the whole is divided into.