A and B together can complete the same work in 36 days. B and C together can complete the same work in 60 days. A and C together can complete the same work in 45 days. In how many days, B alone can complete the same work?

LCM of 36, 60, and 45 will be 180 which can be assumed as the total work.

A and B together can complete the same work in 36 days.

The efficiency of A and B together = $$\frac{180}{36}$$ = 5 units/day

B and C together can complete the same work in 60 days.

The efficiency of B and C together = $$\frac{180}{60}$$ = 3 units/day
A and C together can complete the same work in 45 days.

The efficiency of A and C together = $$\frac{180}{45}$$ = 4 units/day

Efficiecny of A, B and C together = $$\frac{5+3+4}{2}$$ = $$\frac{12}{2}$$ = 6 units/day

Efficiecny of B = (Efficiecny of A, B and C together) - (Efficiency of A and C together)

= 6 - 4

= 2 units/day

The number of days taken by B alone to complete the same work = $$\frac{180}{2}$$

= 90 days