A, B and C together complete a work in 4 days. A and B together finishes the same working days while B alone can do it in 12 days. Now if both A and B started working together and B left after 4 days
Answers
Answer:
A, B, and C together do a job = 4 days
A and C together do the job = 4.5 days = 9/2 days
B and C together do the job = 12 days
Concept used:
Total work = LCM
Formula used:
Efficiency = (Total work)/(Total time)
Calculations:
Efficiency of (A + B + C) : (A + C) : (B + C) = (1/4) : (1/4.5) : (1/12) = 9 : 8 : 3
⇒ Efficiency of C = Efficiency of {(A + C) + (B + C) - (A + B + C)} = 8 + 3 - 9 = 2
We know that, Efficiency is inversely proportional to the time taken.
⇒ (Efficiency of A + B + C) / (Efficiency of C) = (Time taken by C) / (Time taken by A + B + C)
⇒ 9/2 = (Time taken by C)/4
∴ Time taken by C = 18 days
Total work = LCM(4, 9/2, 12) = 36
Person Time Total work Efficiency
A + B + C 4 36 9
A + C 9/2 36 8
B + C 12 36 3
The efficiency of B = 9 – 8 = 1
The efficiency of C = 3 – 1 = 2
Time taken by C alone to complete the work = 36/2 = 18 days
∴ Time taken by C alone to complete the work = 18 days