A, B and C alone can do a piece of work in 11, 33 and 48 days, respectively. They all started the work together, but A left after 2 days. In how many days was the remaining work completed?​

Correct option is C

Given:

A can complete the work in 11 days.

B can complete the work in 33 days.

C can complete the work in 48 days.

A, B, and C all started the work together, but A left after 2 days. 

Formula Used:

Efficiency = $$\frac{\text{Total Work}}{\text{Time Taken}}$$​​

Solution:

Total work = LCM(11, 33, 48) = ​​ = 528 units

Efficiency of A = $$\frac{528}{11} = 48 \, \text{units/day}$$​​

Efficiency of B = $$\frac{528}{33} = 16 \, \text{units/day}$$​

Efficiency of C = $$\frac{528}{48} = 11 \, \text{units/day}$$​

A, B, and C worked together for 2 days.

Combined efficiency of A, B, and C = 48 + 16 + 11 = 75 units/day

Work done in the first 2 days = 75 × 2 = 150 units

Remaining work = 528 − 150 = 378 units

After A left, B and C continued working.

Combined efficiency of B and C = 16 + 11 = 27 units/day

Time taken to complete the remaining work = $$\frac{378}{27} = 14 \, \text{days}$$​​