Problem Solving

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 40 lines on each page which he leaves 25% more margin than before.how much time is now required to type these 23 pages?

Are there answer choices? Here's how I approached it:

1 page, 20 lines, 8% margin, 10 minutes

Of those 20 lines, 8% of the total is blank margin, so the actual amount typed is .92*20=18.4 lines in 10 minutes, or about 1.8 lines per minute.

23 pages, 40 lines, 25% more margin

To figure out out new margin, we simply take the previous amount and add 25% to it: 1.25 * 8 = 10 percent margins.

Using this, we know that 10% of each line is blank, so for 40 lines, the amount typed is 40 * .9 = 36 lines. At a rate of 1.8 lines per minute, each page will take 20 minutes.

All 23 pages will take 23*20 = 460 minutes. Divide by 60 to get to hours and you get 7 2/3 hours.

However, I'd be wary about picking 7 2/3 if it were an option. I rounded from 1.84 lines per minute to 1.8 lines per minute, which means that I used a slightly slower rate and thus got a slightly longer time to complete the work.

If there were an answer like 7 1/2, I would go for that. It is 10 minutes less than 7 2/3, a small change that corresponds to the small rate rounding I did.

shaanGMAT wrote: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 40 lines on each page which leaves 25% more margin than before. how much time is required to type these 23 pages?

a) 7(1/2) hrs
b) 7(2/3) hrs
c) 23(1/2) hrs
d) 3.916 hrs

Case 1:
Let the length of each line = 100 characters.
Since 8% of the left side constitutes a margin, the margin = (8/100) * 100 = 8.
Thus, the number of characters typed per line = 100-8 = 92.
In 20 lines, the number of characters typed = 20*92 = 20*92.
Since the time = 10 minutes, the rate = (20*92)/10 = (2*92) characters per minute.

Case 2:
Since 25% MORE of the left side constitutes a margin, the new margin = 8 + (1/4)8 = 10.
Thus, the number of characters typed per line = 100-10 = 90.
In 40 lines, the number of characters typed = 40*90.
In 23 pages, the number of characters typed = 40*90*23.
At a rate of (2*92) characters per minute, the time required = (40*90*23)/(2*92) = 450 minutes = 7.5 hours.

The correct answer is A.

I followed the following approach:

Assuming every line has 100 characters.

=> with 8% margin, the total number of characters written in one line is 100-8 = 92

Time taken to write 20 lines is 10 mins
=> time taken to write 1 line = 92 characters is 10/(92*20)


Now, when the margin is increased by 25% => new margin is 8+ 0.25*8 = 10
=> number of characters per line now = 90
Total number of characters to be written = number of characters per line * number of lines per page * number of pages = 90*40*23


Total time required = total number of characters * time required to type one character
= (90*40*23)*(10/(92*20)) = 450 minutes = 7 hours and 30 minutes

I guess the key to this question was to break the number of lines into the number of characters so that both the cases have a common decision making variable.

Cheers!