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Math Expert V
Joined: 02 Sep 2009
Posts: 59020
If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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12 00:00

Difficulty:   25% (medium)

Question Stats: 79% (01:47) correct 21% (02:16) wrong based on 305 sessions

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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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Math Expert V
Joined: 02 Aug 2009
Posts: 8157
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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4
Bunuel 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

Typist---------------letters--------------time
--20------------------48------------------20
--20-----------------48*3--------------20*3
--1------------------$$\frac{48*3}{20}$$-----------60 min
--30----------------$$\frac{48*3*30}{20-}$$---------60 min

Answer = $$\frac{48*3*30}{20-}=24*3*3 = 216$$
D
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Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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1
Bunuel 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

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

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Retired Moderator G
Joined: 26 Nov 2012
Posts: 555
If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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1
3
Bunuel 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 have given Man ( typists) , Days , Hours ( time ) and Work ( letters ) and two different MAN DAY cases

Then apply simple formula and very important.

M1 D1 H1 / W1 = M2 D2 H2 / W2. ( Ignore days as this is not mentioned in Question ).

Let the unknown work i.e. no of letters be X and 1 hour = 60 mins.

20 * 20 / 48 = 30 * 60 / X.

X = 216.

Option D.
SVP  B
Joined: 06 Nov 2014
Posts: 1871
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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Bunuel 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

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
Intern  B
Joined: 12 Aug 2013
Posts: 45
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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simple formula of mandays

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

x = 216
Senior Manager  S
Joined: 21 Mar 2016
Posts: 495
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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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: 36
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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Bunuel 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

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  B
Joined: 28 Dec 2010
Posts: 21
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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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.
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Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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Bunuel 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

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

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VP  P
Joined: 07 Dec 2014
Posts: 1222
If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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48/(20*1/3)=36/5=rate of one typist in one hour
30*36/5=216 letters in one hour
Intern  B
Joined: 29 Nov 2016
Posts: 14
Schools: DeGroote
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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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
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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]

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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
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Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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Bunuel 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

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

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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  B
Joined: 03 Aug 2017
Posts: 80
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters  [#permalink]

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Bunuel 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

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 Re: If 20 typists can type 48 letters in 20 minutes, then how many letters   [#permalink] 05 Oct 2019, 22:16
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