Calculate Total Work

Assume Total Work as the Least Common Multiple (LCM) of 80, 40, and 32, which is 160 units.

$\text{LCM}(80, 40, 32) = 160$

Calculate Individual Efficiencies

Efficiency is defined as work divided by time. For A: $160/80 = 2$. For B+C: $160/40 = 4$. For A+C: $160/32 = 5$.

$\text{E}_A = 2, \quad \text{E}_{B+C} = 4, \quad \text{E}_{A+C} = 5$

Isolate B's Efficiency

First find C's efficiency from A+C: $E_C = E_{A+C} - E_A = 5 - 2 = 3$. Then find B's efficiency from B+C: $E_B = E_{B+C} - E_C = 4 - 3 = 1$.

$\text{E}_B = 4 - (5 - 2) = 1$

Calculate Time for B

Time taken by B alone is Total Work divided by B's efficiency.

$\text{Time}_B = \frac{160}{1} = 160$