Calculate Total Work and Efficiencies

Assume total work is the LCM of 12, 15, and 20, which is 60 units. Calculate efficiency (units/day) for each pair.

$Efficiency_{(A+B)} = 5, Efficiency_{(B+C)} = 4, Efficiency_{(A+C)} = 3$

Find Combined Efficiency of A, B, and C

Adding the efficiencies: $2(A+B+C) = 5 + 4 + 3 = 12$. Thus, $A+B+C = 6$.

$A+B+C = 6$

Calculate A's Efficiency

Subtract the efficiency of (B+C) from the combined efficiency of (A+B+C).

$A = (A+B+C) - (B+C) = 6 - 4 = 2$

Calculate Time Taken by A

Divide total work by A's daily efficiency.

$\text{Time} = \frac{60}{2} = 30 \text{ days}$