A can finish a work in 24 days , B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days.The remaining work was done by A in ? any idea please i used work rate concept but i did not reach to the answer
let w represent the work done
A's rate ---- w/24
B's rate ---- w/9
C' rate ----- w/12
B and C's combined rate = w/9 + w/12 = 7w/36
work done by B and C in 3 days
= 21w/36
amount left to be done by A = w - 21w/36 = 15w/36
time for A to finish the job
= (15w/36) / (w/24
= (15w/36)(24/w) = 10 hours
it will be 10 days or 10 hours @ reiny
To solve this problem, we can use the concept of work rates. Let's first find the work rates of each person:
A can finish the work in 24 days, so his work rate is 1/24 work per day (1 job / 24 days).
B can finish the work in 9 days, so his work rate is 1/9 work per day (1 job / 9 days).
C can finish the work in 12 days, so his work rate is 1/12 work per day (1 job / 12 days).
Now, let's calculate the work done by B and C in 3 days:
Work done by B in 3 days = (Work rate of B) × (Number of days) = (1/9) × (3) = 1/3 work
Work done by C in 3 days = (Work rate of C) × (Number of days) = (1/12) × (3) = 1/4 work
The total work done by B and C in 3 days is 1/3 + 1/4 = 7/12 work.
Now, let's determine how much work is left to be done after B and C leave. Since they finished 7/12 of the work, what remains is 1 - 7/12 = 5/12 of the work.
Finally, we can calculate the time taken by A to finish the remaining 5/12 of the work. Using A's work rate of 1/24 work per day, we can set up the equation:
(Work rate of A) × (Number of days) = (Work left to be done)
(1/24) × (Number of days) = 5/12
Now, we can solve for the number of days:
Number of days = (5/12) / (1/24) = (5/12) × (24/1) = 10
Therefore, A would take 10 days to complete the remaining 5/12 of the work after B and C leave.
The answer is 10 days.