Three friends are building a model city for an exhibition. Ananya and Bilal together would take 10 days, Bilal and Charu 15 days, and Charu and Ananya 12 days. How many days would all three take working together?

Explanation

1. 01

   Add the three pair rates: $\frac{1}{10} + \frac{1}{15} + \frac{1}{12} = \frac{6+4+5}{60} = \frac{1}{4}$.

2. 02

   Each person is counted twice, so the three together do $\frac{1}{4} \div 2 = \frac{1}{8}$ per day.

3. 03

   All three finish in 8 days.