‘A’ alone can complete a piece of work in 30 days while ‘A’ and ‘B’ together can complete the same work in 20 days. ‘B’ started the work and after 4 days ‘A’ joined him. After 6 more days, ‘A’ left and ‘C’ joined the work and the whole work was completed in 22 days.
Which one of the following statement is true?

Time taken by ‘A’ to complete the whole work = 30 days

Let total amount of work = 300 units (LCM of 30 and 20)

So, efficiency of ‘A’ = 300/30 = 10 units per day

Efficiency of ‘A’ + ‘B’ = 300/20 = 15 units per day

Efficiency of ‘B’ = 15 – 10 = 5 units per day

Amount of work done by ‘B’ in 4 days = 5 × 4 = 20 units

Amount of work done by ‘A’ and ‘B’ together in 6 days = 6 × 15 = 90 units

Amount of work done by ‘B’ and ‘C’ together in 12 days = 300 – 20 – 90 = 190 units

So, efficiency of ‘B’ and ‘C’ together = 190/12 ≈ 15.83 units per day

Efficiency of ‘C’ ≈ 15.83 – 5 ≈ 10.83 units per day

For option (a):
Amount of work done by ‘A’ in 12 days = 12 × 10 = 120 units
Amount of work done by ‘B’ in 8 days = 8 × 5 = 40 units
Remaining work = 300 – 120 – 40 = 140 units
Time taken by ‘C’ = 140/10.83 ≠ 10 days

So, option (a) cannot be the answer.

For option (b):
Efficiency of ‘C’ ≈ 2 × 10.83 ≈ 21.66 units per day
Time taken = 300/21.66 ≠ 18 days

So, option (b) cannot be the answer.

For option (c):
Desired time = (0.60 × 300)/(10 + 10.83) ≠ 8 days

So, option (c) cannot be the answer.

Hence, option e.