Problem Solving

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?

1 hour and 34 minutes
1 hour and 45 minutes
2 hours and 24 minutes
3 hours and 15 minutes
3 hours and 25 minutes

OA D

crackgmat007 wrote: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?

1 hour and 34 minutes
1 hour and 45 minutes
2 hours and 24 minutes
3 hours and 15 minutes
3 hours and 25 minutes

OA D

Hi crackgmat007,

Their speeds are in a 4:3:2 ratio. So, if we split the job into 9 (4+3+2) parts, the fastest secretary will have contribued 4/9 towards the job, the middle one 3/9, and the slowest secretary contributed 2/9 towards the job.

So, the slowest secretary manages 2/9 of 36 pages in a half an hour: 2/9 * 36 = 8 pages in a half an hour. Then, her rate per hour is 16 pages per hour.

It will take her 52/16 = 3.25 hours, or three hours and fifteen minutes to type 52 pages. Choose D.

let total x no. of pages
in 1 hr they will type
4x+3x+2x = 72 pages
x = 8
1st type = 4*8 = 32 pages/hr
2nd type = 24 pages/hr
3rd type = 2*8 = 16 pages/hr
So, for typing 52 pages
3 will take
3hr = 48 pages
and for 4 pages = 1/4hr = 15min
hence 3 hrs 15 min
Ans is D/