A and B can do a piece of work in 10 days. B and C can do the same work in 12 days. C and A can do the same work in 15 days. If all the three work together, find the number of days required to complete the work.

Let the total work be the LCM of 10, 12, and 15, which is 60 units.
Calculating individual combined efficiencies per day:

Efficiency of (A+B)=
10
60
​
=6 units/day

Efficiency of (B+C)=
12
60
​
=5 units/day

Efficiency of (C+A)=
15
60
​
=4 units/day

Adding all three equations:

2(A+B+C)=6+5+4=15 units/day
Efficiency of (A+B+C)=
2
15
​
=7.5 units/day
Number of days required by A, B, and C working together:

Days=
Total Efficiency
Total Work
​
=
7.5
60
​
=
15
60×2
​
=8 days