WOrk and typists

maihuna wrote:P Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour R can type as many pages more than Q as Q can type more than P. During a period of 5 hours, R can type as many pages as P can during 7 hours, How many pages each of them type per hour:

14, 17, 20
15, 17, 19
15, 18, 21
16, 18, 20
16, 19, 22

Choose C.

dtweah wrote:

maihuna wrote:P Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour R can type as many pages more than Q as Q can type more than P. During a period of 5 hours, R can type as many pages as P can during 7 hours, How many pages each of them type per hour:

14, 17, 20
15, 17, 19
15, 18, 21
16, 18, 20
16, 19, 22

Choose C.

I actually love this problem. On the phase of it it looks intimidating but when you dig into it, it is not. Stick with principles:

Let R, P and Q be the job each do in 1 our respectively.
If they do 216 in 4 hours, find how many they do in 1 hour.

216/4=54.

So you know R +P+Q=54 --------(1)

In one hour R can type as many pages as Q as Q can type many pages more than P. This is Mathematese for

R-Q=Q-P
R= 2Q-P -----(2)

Comes another confusing joint: During a period of 5 hours, R can type as many pages as P can during 7 hours.

But we know P is number P can do in 1 hour. So 7P is what he will do in 7 hours.
Since R is the number R can do in 1, in 5 hour R will do 5R.

Then 5R=7P -----(3)

2Q-P+P+Q=54
Q=18

R=36-P

But P = 5R/7

So R= 21

54-39=15

Choose C.

grt u rock sir

During a period of 5 hours, R can type as many pages as P can during 7 hours

=>5R=7P
=>R/P=5/7

14, 17, 20 doesnt give 5/7
15, 17, 19 doesnt give 5/7
15, 18, 21 ..15/21=5/7 bingo
16, 18, 20 doesnt give 5/7
16, 19, 22 doesnt give 5/7

hence, C

scoobydooby wrote:During a period of 5 hours, R can type as many pages as P can during 7 hours

=>5R=7P
=>R/P=5/7

14, 17, 20 doesnt give 5/7
15, 17, 19 doesnt give 5/7
15, 18, 21 ..15/21=5/7 bingo
16, 18, 20 doesnt give 5/7
16, 19, 22 doesnt give 5/7

hence, C

Cool. To switch from fully solving a problem to using one of the equations you discover to resolve the answer choices takes more than sheer guts. This example points to the fact that in thinking about solutions, the answer choices must always be on your mind. Good trick Scooby.

good explanations guys!!

M