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Manager  Joined: 06 Jul 2011
Posts: 84
If two typists can type two pages in two minutes, how many t  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 65% (01:29) correct 35% (01:36) wrong based on 657 sessions

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If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?

A. 3
B. 4
C. 6
D. 12
E. 36

Could anyone plz explain a robust approach to solve above mentioned problem.I mostly get confused in RT=W probs.Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 55732
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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8
2
arkle wrote:
If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?

A. 3
B. 4
C. 6
D. 12
E. 36

Could anyone plz explain a robust approach to solve above mentioned problem.I mostly get confused in RT=W probs.Thanks!

Since two typists can type two pages in two minutes, then one typists can type two pages in four minutes, which means that the rate of one typist is $$rate=\frac{job}{time}=\frac{2}{4}=\frac{1}{2}$$ pages per minute.

Now, (combined rate of x typists)*(time)=(job) --> $$(\frac{1}{2}*x)*6=18$$ --> $$x=6$$.

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Re: Approach to solve Rate,Time work problems  [#permalink]

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5
If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?
3
4
6
12
36

Suppose rate of each typist is R
So rate of two typist will be 2R
time = 2mins
work = 2pages
using : Rate * Time = Work ,we have:
2R * 2 = 2
=> R = 0.5 pages/min

Suppose x number of typist are required to finish 18pages in 6mins
So, rate of R typist will be xR
Time = 6mins
work = 18pages
Using Rate*time= work we have

xR * 6 = 18
=> xR = 3
we know that R =0.5
=> x = 6

Hope it helps!
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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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1
arkle wrote:
If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?

A. 3
B. 4
C. 6
D. 12
E. 36

Could anyone plz explain a robust approach to solve above mentioned problem.I mostly get confused in RT=W probs.Thanks!

2 typists 2 pages 2 minutes
2 typists 2*9=18 pages 2*9=18 minutes (9 times more pages, 9 times more time)
2*3=6 typists 18 pages 18/3=6 minutes (need 3 times faster, should increase number of typists by the same factor 3)

This question is about direct and inverse proportionality.
RxT=W (rate x time = work)

If work is constant, then R and T are inversely proportional, meaning if R increases, T decreases and vice-versa.
If R is constant, then T and W are directly proportional, meaning if T increase, W increases (more time, more job done).
If T is constant, then R and W are again directly proportional, meaning if R increases, W increases (faster rate, more job done).

In the above approach, first if we increase the number of pages (more work must be done), but we stay with the same number of typists, we need proportionally more time. Here, time and work are directly proportional.
Then, for the same number of pages (same work), if we want the job done faster, we need more typists. Now, number of typists and time are inversely proportional.

This type of question reminds me of a home-work that would upset many parents (lamenting that this is insane ):

If one and a half chicken lay in a day and half one egg and a half, how many eggs will lay three chicken in three days?

Who heard of half chickens laying half eggs...those math teachers gone mad!!!
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Senior Manager  Joined: 13 Aug 2012
Posts: 416
Concentration: Marketing, Finance
GPA: 3.23
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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Let the individual rate of each typist be=$$\frac{1}{t}$$

Using the Rate equation Rt=W we can calculate their rates:
$$(\frac{1}{m}+\frac{1}{m})(2 minutes)=2pages==>\frac{2}{m}=\frac{2pages}{2minutes}==>m=2minutes$$

Thus, the individual rate of each typist =$$\frac{1page}{2minutes}$$

Now let's calculate the number of typists needed to work for 6 minutes to make 18 pages.

$$\frac{N}{2minutes}(6min)=18pages==>N=\frac{18}{3}=6$$

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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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To handle this type of problem efficiently I like to extend the R(T)=W formula ==> to #RT=W where # is number of people and RTW is still Rate, Time, Work. So for this problem:

Solve for R first
#=2 typists
R=?
T=2 minutes
W=2 pages

#RT=W==>2(R)(2)=2==>4(R)=2 divide both sides by 4 to get R=2/4 which is of course R=1/2. Now you have the rate PER TYPIST.

Now solve the rest of the question the same way to get #
#=?
R=1/2
T=6 minutes
W=18 pages

#RT=W==>#(1/2)(6)=18==>#(3)=18 divide both sides by 3 and you get #=6. So 6 is the number of typists it will take to accomplish 18 pages in 6 minutes. Hope it helps.
Intern  Joined: 16 Jan 2013
Posts: 20
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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1
More the no. of pages, more the no. of typist required.
more the minutes available, lesser the no. of typist required.
therefore, no. of typist is directly proportional to the no. of pages and inversely proportional to the no. of minutes
Hence, No of typist = 2x(18/2)x(2/6) = 6
Intern  Joined: 20 Feb 2013
Posts: 20
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?

A. 3
B. 4
C. 6
D. 12
E. 36

In 2 minutes 2 typists type 2 pages which means that in 6 minutes they will type 6 pages but to type 18 pages (3 times) we need 3 times more typists i.e. 2 x 3 = 6 typists.

OR (A more structured approach)

2 Typists ------- 2 pages ---------- 2 minutes

2 Typist --------- 1 page ----------- 1 minutes

1 Typist --------- 1/2 page --------- 1 minute

1 Typist --------- 3 pages ----------- 6 minutes

6 Typists -------- 18 pages --------- 6 minutes

OR
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Pushpinder Gill
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Posts: 30
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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Bunuel wrote:
arkle wrote:
Since two typists can type two pages in two minutes, then one typists can type two pages in four minutes,

Hi Bunuel,
Can we conclude that the efficiency of both typists are same?
Regards,
Pritish
Intern  Joined: 24 Sep 2012
Posts: 30
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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Yes is clear. Thank you!
Intern  Joined: 20 Feb 2013
Posts: 20
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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pritish2301 wrote:
Bunuel wrote:
arkle wrote:
Since two typists can type two pages in two minutes, then one typists can type two pages in four minutes,

Hi Bunuel,
Can we conclude that the efficiency of both typists are same?
Regards,
Pritish

Yes you can assume both the typists to be equally efficient.
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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?

A. 3
B. 4
C. 6
D. 12
E. 36

SOLUTION:

Work = Rate*Time
2 pages = R*2 min
i.e. R = 1 page/min for 2 typist ---- (i)

18 pages = R*6 min
i.e. R = 3 pages/min for N typists ---- (ii)

Eq.(ii) = 3*(i) i.e. N typists are 3x faster than 2 typists. Therefore N = 2*3 = 6 typists

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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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Rate per typist per page $$= \frac{2}{2*2} = \frac{1}{2}$$

Rate ............... No. of typists .............. Time ............ Pages(Work done)

$$\frac{1}{2}$$ ..................... x ........................... 6 ................... 18

$$x = \frac{18}{6} * 2 = 6$$

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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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arkle wrote:
If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in six minutes?

A. 3
B. 4
C. 6
D. 12
E. 36

Could anyone plz explain a robust approach to solve above mentioned problem.I mostly get confused in RT=W probs.Thanks!

Including the number of ppl in the RT equation

Given 2*R*2 = 2; so R=1/2;

Now N*1/2*6=18; N=18/3 = 6

So Ans:C
Manager  S
Joined: 22 Nov 2016
Posts: 205
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GPA: 3.4
Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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2 typists - 2 pages - 2 mins
1 typist - 1 page - 2 mins
1 typist - 1/2 page -1 min

W = 18 ; T=6, R=x*1/2 (x is the number of typists needed to type at a rate of 1/2)
W=RT
x=3
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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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or use the formula
M1XT1/J1=M2XT2/J2

M1=manpower=2
T1=time=2mins
J1=Job=2 pages

M2=?
T1=6mins
J1=18 pages

2X2/2=M1X6/18=6 Ans=c
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Re: If two typists can type two pages in two minutes, how many t  [#permalink]

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_________________ Re: If two typists can type two pages in two minutes, how many t   [#permalink] 01 Dec 2018, 10:53
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