A can do a piece of work in 12 days. B can do it in 18 days. With the assistance of C, they completed the work in 4 days. C alone can do it in ________ days.

Given:

A can do the work in 12 days.

B can do the work in 18 days.

A, B, and C together can complete the work in 4 days.

Formula Used:

Total Work = LCM of (Time taken by A, Time taken by B, Time taken by A+B+C)

Efficiency = Total Work / Time taken

Calculation:

Total Work (LCM of 12, 18, and 4):

Prime factorization of 12 = 2² × 3

Prime factorization of 18 = 2 × 3²

Prime factorization of 4 = 2²

LCM(12, 18, 4) = 2² × 3² = 4 × 9 = 36 units

Efficiency of A (E_A) = Total Work / Time taken by A = 36 / 12 = 3 units/day

Efficiency of B (E_B) = Total Work / Time taken by B = 36 / 18 = 2 units/day

Efficiency of (A + B + C) = Total Work / Time taken by (A+B+C) = 36 / 4 = 9 units/day

Efficiency of C (E_C):

E_A+B+C = E_A + E_B + E_C

9 = 3 + 2 + E_C

9 = 5 + E_C

E_C = 9 - 5 = 4 units/day

Time taken by C = Total Work / E_C = 36 / 4 = 9 days

∴ C alone can do it in 9 days.