Word Problem in Work and Time

Work Time is a topic in which quite a few interesting word problems are found.

Two typists are engaged to type 720 pages. Typist A takes 11 more hours than typist B to type 720 pages. If typist B types 20% more pages per hour than typist A, in how many hours will the task be completed if both A and B work together on the task?
A. 330 hours
B. 66 hours
C. 30 hours
D. 55 hours
E. 11 hours

Explanatory Answer

Let typist B take t hours to complete task.

Typist A takes 11 more hours than typist B. So, typist A will take (t + 11) hours to complete the task.

Let typist A type ‘n’ pages each hour.

Typist B types 20% more pages per hour than typist A.

So, typist B will type n + 20% of n = pages in an hour.

Typist A works (t + 11) hours typing n pages each hour to type 720 pages.

i.e., (t + 11)n = 720.

Typist B works t hours typing  pages each hour to type 720 pages.

So, 

Dividing both sides of the equation by ‘n’ and cross multiplying 10, we get 10(t + 11) = 12t

or 2t = 110 or t = 55. t is the time taken by typist B to type 720 pages.

Typist A will take (t + 11) = (55 + 11) = 66 hours to type 720 pages.

If they work together, the two typists will type pages each hour.

Or  pages each hour.

i.e., pages each hour.

Together, they will type 24 pages each hour.

So, typists A and B will complete the task in  = 30 hours.

Choice C is the correct Answer