A Problem of Typing

It was a day of rush. I had to send off the typescript to my publisher by the evening's mail. Mr Das Gupta, my stenographer is a very experienced person and he, I knew, could do the job neatly and quickly. 
But even he would take 2 hours to finish the job. This couldn't have been done! So I decided to engage another typist. She would do a neat job, I was told, but she was not a fast typist like Mr Das Gupta. She looked at the job and said that if she were to do the entire job by herself, it would take her three hours. 
I decided to let them do the job side by side. Within how much time, can you tell, the two of them finished the work?

First of all let us find out how the typists should divide the job to finish it at the same time. 
The more experienced typist, Mr. Das Gupta, can work 1½ times faster than the other. Therefore it is clear that his share of work should be 1½ times greater. 
Then Mr Das Gupta as well as the new lady typist will both finish the work simultaneously. 
Hence Mr Das Gupta should take ⅘ of the work and the lady typist ⅖. This solves the problem, but there still remains for us to find how long it takes Mr. Das Gupta to do his share i.e. ⅗ of the work. 
We know that he can do the whole job in two hours. Therefore ⅗ of job will be done in ⅗ × 2 = 1⅕ hours. So the other typist also must finish her share of work within the same time. Therefore the fastest time they can finish the work is 1 hour and 12 minutes.