A.B. C can finish one task in 24 days, 32 days and 64 days respectively, they work together in a joint. a 6 days later the job goes away and B is left 6 days before the work ends. How many days did this work end?
Answers
Answer:
Total number of days = 20
Step-by-step explanation:
It is given that, A.B. C can finish one task in 24 days, 32 days and 64 days respectively
To find the LCM of 24,32,and 64
LCM(24,32,64) = 192
To find efficiency of A,B and C
efficiency of A = 192/24 = 8
efficiency of A = 192/32 = 6
efficiency of A = 192/64 = 3
To find the number of days
One day work of A, B and C together = 8+6+3 = 17
6 days they together work, then total work completed after 6 days = 6 * 17 = 102.
Last 6 days C's work =6*efficiency of C = 6 * 3 = 18
Therefore the 12 days work = 102 + 18 = 120
Then the remaining work = 192 - 120 = 72
This work completed by B and C
Number of days taken by B and C = 72/(efficiency of B and C) = 72/9 = 8 days
Therefore total number of days = 6 + 8 + 6 = 20 days
The remaining work