Last visit was: 14 Sep 2024, 07:46 It is currently 14 Sep 2024, 07:46
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If 20 typists can type 48 letters in 20 minutes, then how many letters

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 95503
Own Kudos [?]: 658489 [30]
Given Kudos: 87257
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11510
Own Kudos [?]: 36008 [9]
Given Kudos: 333
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 503 [6]
Given Kudos: 46
General Discussion
SVP
Joined: 06 Nov 2014
Posts: 1791
Own Kudos [?]: 1387 [1]
Given Kudos: 23
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
1
Kudos
Bunuel
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

It is always better to find out the time needed for typing one letter in such problems.

Total typist minutes required to type 48 letters = 20*20 = 400 minutes.
Time needed for each letter = 48/400 minutes.

Number of letters completed by 30 typists in 60 minutes = (48/400) * 30*60 = 216 letters.

Correct Option: D
Current Student
Joined: 18 Oct 2014
Posts: 679
Own Kudos [?]: 1807 [2]
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
1
Kudos
1
Bookmarks
Bunuel
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

20 typists can type 48 letters, so 30 typists can type = 48*30/20

48*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 48*30*60/20*20= 216

Intern
Joined: 12 Aug 2013
Posts: 43
Own Kudos [?]: 24 [0]
Given Kudos: 0
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
simple formula of mandays

(20*20)/(60*48) = (30*1)/x

x = 216
Senior Manager
Joined: 21 Mar 2016
Posts: 448
Own Kudos [?]: 123 [0]
Given Kudos: 103
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
20 typist type 48 letters, so 30 typists type = (48/20) * 30 letters in 20 mins.

in 60 mins 30 typists type, = (48/20*20) * 30 * 60 = 216

Intern
Joined: 01 May 2015
Posts: 32
Own Kudos [?]: 140 [0]
Given Kudos: 1
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
Bunuel
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
20 typists can type 48*20 letter minutes
20*20 typist-minutes is equal to 48 letters
1 typist-minute is equal to 48/(20*20) letters
30*60 typist-minutes is equal to 48*30*60/(20*20) letters =216 letters.
Intern
Joined: 28 Dec 2010
Posts: 19
Own Kudos [?]: 235 [0]
Given Kudos: 337
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
The question is asking about the amount of work done in 60 mins or 1 hours. Using this information we can calculate, the amount of work done by 20 typists in 60 minutes 3 (20)*48 = 144 words. Now we can use the unitary method to find the work done by 30 typists in 60 mins i.e. 144/20*30 = 216 word.

Tip: For a fixed time more men imply more work. (considering work done by each man is consistent) therefore, we can also eliminate answer choice A, B, C.
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6046
Own Kudos [?]: 4822 [0]
Given Kudos: 463
Location: India
GPA: 3.5
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
Bunuel
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

20 typists can type 48 letters in 20 minutes

So, working at same pace 20 typists can type 48*3 letters in 1 hour (20*3 minutes)
Or, 20 typists can type 144 letters/hr
So, Efficiency per worker is 144/20

If 30 workers are employed , they can produce = 144/20*30 =>216 letters

VP
Joined: 07 Dec 2014
Posts: 1064
Own Kudos [?]: 1654 [0]
Given Kudos: 27
If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
48/(20*1/3)=36/5=rate of one typist in one hour
30*36/5=216 letters in one hour
Intern
Joined: 29 Nov 2016
Posts: 14
Own Kudos [?]: 5 [2]
Given Kudos: 86
Schools: DeGroote
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
1
Kudos
1
Bookmarks
I used ratios
typers:letters:mins
20:48:20
first converted 20 mins into one hour by multiplying by 3
Letter:mins
48(3):20(3)
144:60 mins

then to make the 20 equal to 30 typers i multiplied by 3/2 and also multiplyed 3/2(144)
typers : letters
20(3/2) = 30 typers : 144(3/2) = 216 letters
30 typers: 216 letters
Current Student
Joined: 04 Jan 2016
Posts: 158
Own Kudos [?]: 113 [0]
Given Kudos: 421
Location: United States (NY)
GMAT 1: 620 Q44 V32
GMAT 2: 600 Q48 V25
GMAT 3: 660 Q42 V39
GPA: 3.48
If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
20 machines times their constant respective rate in 20 minutes can produce 48 letters. Therefore, $$20*(r) * 20 = 48,$$
Rate$$(r)=\frac{48}{20} * \frac{1}{20} => r= \frac{48}{400}$$

30 machines in 1 hour (60 minutes) will produce how many letters:

$$30 * \frac{48}{400} * 60 = 3*\frac{48}{4}*6 = 18*12=216$$

Option: D
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19460
Own Kudos [?]: 23238 [2]
Given Kudos: 286
Location: United States (CA)
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
2
Bookmarks
Bunuel
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

Intern
Joined: 16 May 2017
Posts: 39
Own Kudos [?]: 18 [0]
Given Kudos: 78
GPA: 3.8
WE:Medicine and Health (Health Care)
If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
For 20 typists, work rate=48/20= 2.4 letters/min
For 1 typist, work rate= 2.4/20 letters/min

For 30 typists, total letters typed in a min=2.4/20*30= 3.6 letters
So, letters typed in 60 mins=60*3.6= 216 letters

(D)
Manager
Joined: 03 Aug 2017
Posts: 76
Own Kudos [?]: 26 [0]
Given Kudos: 85
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
Bunuel
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

This i how i solved...

20 Typist can type 48 letters / 20 Min therofre in 1 Min 20 Typist can type = 48/20 = 2.4 Letters per Min
In 60 Min 20 Typist can type = 2.4 *60 =144 Words per min...

We are also told now there are 30 Typist so if 20 typist can type 144 words so 30 Typist can type X words per min.....

Solve for X
20/144 = 30 / x .....
x = 72*3 = 216 Words per min
Intern
Joined: 14 Nov 2022
Posts: 16
Own Kudos [?]: 10 [0]
Given Kudos: 10
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
48[letters] = 20[minutes]*(20[typers]/Rate[minutes/letters]) --> Rate = 400/48

X[letters] = 60[minutes*(30[typers]/Rate[minutes/letters]) --> 60[minutes*(30[typers]/(400/48))

X[letters] = 60*30*48/400 = 216
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31311 [1]
Given Kudos: 799
If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
1
Kudos
Top Contributor
Bunuel
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

Given: 20 typists (workers) can type 48 letters (output) in 20 minutes (time).
So, 20 typists (workers) can type 144 letters (output) in 60 minutes (time). [If you triple the time, the output also triples]
So, 30 typists (workers) can type 216 letters (output) in 60 minutes (time). [If you increase the number of workers by 50%, the output also increase is by 50%]

Non-Human User
Joined: 09 Sep 2013
Posts: 34831
Own Kudos [?]: 878 [0]
Given Kudos: 0
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
Moderator:
Math Expert
95503 posts