If two typists can type two pages in two minutes, how many t

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)

Answer C

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!!!

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.

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

Answer: C

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.

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

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

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

Yes is clear. Thank you!

Yes you can assume both the typists to be equally efficient.

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

ANSWER: c

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

\(x = \frac{18}{6} * 2 = 6\)

Answer = C = 6

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

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

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

To solve it in a simple way,
2 pages written in 2 minutes by 2 typist
1 page written in 1 minutes by 2 typist
18 pages written in 18 minutes by 2 typist

18 pages written in \(18/3\)=6 minutes by \(2*3\)=6 typist

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