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Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text?

(A) 1 hour and 34 minutes (B) 1 hour and 45 minutes (C) 2 hours and 24 minutes (D) 3 hours and 15 minutes (E) 3 hours and 25 minutes

Three secretaries working together can type 36 pages in half an hour. If the typing speeds of the secretaries are in 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages?

Please explain. Thanks.

4x+3x+2x=72 (1hr) 9x=72 --x=8. The slowest is 2(8) 16pgs in 1 hr.

You have typing speeds for each secretary as follows 4:3:2. Lets say secretary A, secretary B and secretary C respectively. So A has a speed of 4x, B of 3x and C of 2x

The three of them could write 36 pages in half hour so: 36 pages = A effort + B effort + C effort 36 = 4x + 3x + 2x x = 4

So we derive that the secretary C could finish 2x of work that would be 8 pages in the half hour So for C how much would it take to write 52 pages?

Lets find how many pages were completed per individual in those 36pages in 30mins

4x + 3x + 2x = 36 9x = 36 x = 4

So the slowest person would be 2x...which only did 8 pages in those 30mins The question is asking how long it would take this person to type 56 pages well 8pages * 6 = 48pages remember it is 8 pages for every 30mins so 6*.5 = 3 hours with a left over of 4 pages which is half of 8pages therefore it would be half the mins...30mins/2 = 15mins

in the end we get 3hrs and 15mins Choice D...this is my exact thought process. there is probably a better way to figure this out after you get x = 4

Here is my solution; lets say x pages were completed per individual in those 36pages in 30mins (x is speed in page per min) 4x + 3x + 2x = 36/30 p/m 9x = 36/30 p/m x = 4/30 p/m =4p/30m

So the slowest person would be 2x = 8p/30m since slowest person needs 30 min for 8 pages or, he can complete 8 page in 30 min for 52 page he needs =30*52/8 = 195min = 3 hr 15 min.

Choice D..
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Rate * Time = work Rate *1/2 = 36 Rate = 72. Problem stated that the rates of the 3 members are in the ratio 0f 4:3:2. we need rate for the smaller worker which is 2/9.

So 72*2/9 =16 (rate of the smaller worker). Again back to the formula: Rate * Time = work 16* X= 52 X=52/16=26/8=3.25 (3 hour 15 minutes)

It takes 3 secretaries 30mins to type 36 pages at a ratio of 4:3:2 pages per secretary, e.g. the fastest types 16 pages in 30 mins, the middle one types 12 pages in 30mins, and the slowest one types 8 pages in 30mins, or she will take 3.75mins per page.

So, 3.75min/page x 52 pages = 195mins or 3hrs 15mins.

I did the question as most others did and got to D within a minute to a minute and a half.

Personally I do not feel that this is a 700 level question, however, seeing as they make the test and define its difficultly they would be the final authority on this topic. 700+ it is.

answer D 3 secretary working together types 36 pages in 30 mins 3 secretary working together will type 72 pages in 60 mins ratio of typing speed 4:3:2 , so assuming x is the no. of pages then 4x+3x+2X = 72 pages/hr 9x=72page/hr X=8page/hr, slowest person types 2x times so 16 pages/hr or 4page/15mins so 52 pages will be 52/4= 13(15mins) which equals 3 hour and 15mins alternately 52 pages will be types in 16/hr*3 = 48page/3hours + 4page /15mins = 52 page in 3hr & 15mins

slowest secretary contributes 2/9th of the quantities in half an hour = 36X2/9 = 8 pgs in half hour or 16 pages in 1 hr. hence to produce 52 pages it will take 52/16 = 3 hrs and 15 mins.

Cheers everyone this is my first post and 1st day of GMAT prep.. +1 for D -Total Time taken for 36 pages is 30 minutes I.e overall typing speed is 36/30=1.2 page/minute -Now considering slowest typing speed ratio w.r.t total speed we get 2/9 (slowest speed/overall) -To type 52 pages overall time will be 52(pages)/1.2(pages/minute)=43.4 minutes Therfore multiplying the slowest time ratio of 9/2 to overall time will lead to slowest individual time taken I.e. 195 mintes 3hr 15 min