A and B can do a piece of work in 12 days. B and C can do the same work in 8 days. They can complete the work in 6 days if they work together. Find the number of days in which B can alone complete the work
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A and B can do the work in 12 days:
⇒ 1 day = 1/12 of the work
B and C can do the work in 8 days:
⇒ 1 day = 1/8 of the work
A, B and C can do the work in 6 days
⇒ 1 day = 1/6 of the work
Find the amount of work B can do in a day:
( A + B) + ( B + C) - ( A + B + C ) = A + B + B + C - A - B - C = B
1 day = 1/12 + 1/8 - 1/6 = 1/24
Number of days B will need to complete the work alone:
1/24 of the work = 1 day
24/24 of the work = 1 x 24 = 24 days
Answer: B will need 24 days to complete the work.
ashgreninja31:
How
Which part do you not understand? Allow me to elaborate more on that ...
last part
Number of days B will need to complete the work alone?
24/24 this part
24/24 = 1 , which is the work itself
if he can do only 1/24 of the work a day, he will need 24 days to complete the work.
1/12 +1/8-1/6
( A + B) + ( B + C) - ( A + B + C ) = A + B + B + C - A - B - C = B
(A + B) = 1/2
(B + C) = 1/8
(A + B + C) = 1/6
So if we add the first 2 and subtract the 3rd, we will get B only.
(B + C) = 1/8
(A + B + C) = 1/6
So if we add the first 2 and subtract the 3rd, we will get B only.
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