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typists working at the same rate

by sanju09 » Mon Oct 24, 2011 1:57 am
If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
a. 63
b. 72
c. 144
d. 216
e. 400


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by neelgandham » Mon Oct 24, 2011 2:52 am
20 typists can type 48 letters in 20 minutes,

Implies, 1 Typist can type 48/20 letters in 20 minutes.
Implies, 1 Typist can type 48/(20*20) letters in 1 minute.
Implies, 30 Typists can type (48*30)/(20*20) letters in 1 minute.
Implies, 30 Typists can type (48*30*60)/(20*20) letters in 60 minutes(An hour).

(48*30*60)/(20*20) = [spoiler]12*18 = 216[/spoiler]. Answer : D
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by MBA.Aspirant » Mon Oct 24, 2011 2:52 am
D) 216
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by GMATGuruNY » Mon Oct 24, 2011 3:08 am
sanju09 wrote:If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
a. 63
b. 72
c. 144
d. 216
e. 400


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Look for an easy way to convert:

20 typists producing 48 pages in 20 minutes
implies
10 typists producing 24 pages in 20 minutes
which implies
3*10 = 30 typists producing 3*24 = 72 pages in 20 minutes
which implies
30 typists producing 3*72 = 216 pages in 3*20 = 60 minutes.

The correct answer is D.
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by vaibhavgupta » Mon Oct 24, 2011 3:24 am
sanju09 wrote:If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
a. 63
b. 72
c. 144
d. 216
e. 400


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by atnt444 » Mon Oct 24, 2011 4:06 pm
20 people take 20 min to type 48 letters ,so in 60 minutes these people will type (48*3) or 48+48+48 == 144 letters . This leaves us with D and E .

At this stage we can take a decent guess that 10 people at the same rate can not take it to 400 and the answer is D .

To be on the safer side 10 people will type 24 letters in 20 minutes and that adds to 72 in 60 min. So the total is 144+72 (216)
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by ravirajsitaram » Tue Oct 25, 2011 4:39 am
20 typists , 20 minutes - 48 letters.. 1 typist 1 min -- 48 / (20 * 20)
30 typists , 60 minutes = 48 * 30 * 60 / (20 * 20)
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by Scott@TargetTestPrep » Wed Aug 01, 2018 3:21 pm
sanju09 wrote:If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
a. 63
b. 72
c. 144
d. 216
e. 400
We can set up a proportion to determine the rate n (number of letters per minute) of 30 typists.

20 typists / rate of those 20 typists = 30 typists / (unknown) rate of those 30 typists

20/(48/20) = 30/n

20/(12/5) = 30/n

100/12 = 30/n

100n = 12 x 30

10n = 12 x 3

10n = 36

n = 3.6

We see that the rate of 30 typists is 3.6 letters per minute. So in 60 minutes, 30 typists can complete 3.6 x 60 = 216 letters.

Alternate Solution:

We know that 20 typists can type 48 letters in 20 minutes. Thus, we see that in 60 minutes, or 1 hour, those 20 typists can type 3 times as many letters, or 3 x 48 = 144 letters. We can now set up a proportion for n = the number of letters that can be typed in 1 hour by 30 typists:

20/144 = 30/n

20n = 144 x 30

2n = 144 x 3

n = 216

Answer: D

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