Working in pairs on a mural, Deepa and Elango take 12 days, Elango and Farhan take 20 days, and Deepa and Farhan take 15 days. How many days would Farhan take working alone?

Explanation

1. 01

   Sum of pair rates: $\frac{1}{12} + \frac{1}{20} + \frac{1}{15} = \frac{5+3+4}{60} = \frac{1}{5}$.

2. 02

   All three together: $\frac{1}{5} \div 2 = \frac{1}{10}$ per day.

3. 03

   Farhan = all three − (Deepa + Elango) = $\frac{1}{10} - \frac{1}{12} = \frac{1}{60}$.

4. 04

   Farhan alone takes 60 days.