Help with case question

A doctor spends 75% of his time on patient care, 15% on billing, and 10% on administrative overhead, and his total revenue is 425,000$. If he uses a new billing service, he can allocate the 15% of the time he used to spend on billing to looking after patients. What will his revenue be if he makes that change?

The solution given for the revenue he is going to get by using the billing service is this:

(425,000*0.15)/0.75 = $85,000

I get why we need to find 15% of 425,000, but why do we then divide by 75%? Can anyone explain the reasoning behind this calculation?

3 Comments
 

I'm thinking about it as he spends 75% of his time doing revenue generating tasks. Post billing software he spends 90% of his time doing revenue generating tasks (75%+15%). His new revenue will be 90/75x425000. If we want to find the change we would do (90-75)/75x425000 or .15/.75x425000.

 

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