A and B can complete a task together in 35 days. If A completes 5/7 of the task and then leaves the rest for B, it will take a total of 90 days to complete the task. How many days would it take A to complete the entire work by herself?
Answers
Step-by-step explanation:
A and B can complete a task together in 35 days. If A completes 5/7 of the task and then leaves the rest for B, it will take a total of 90 days to complete the task. How many days would it take A to complete the entire work by herself?
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Let us assume that A completes the work alone in X number of days.
Work done by A and B in 1 day = 1/35 (given)
Work done by A alone in 1 day = 1/X
Work done by B alone in 1 day = (1/35) - (1/X) = (X - 35) / 35X
No. Of days taken by A for doing 5/7 of work = (5/7) / (1/X) = 5X/7 days.
No. Of days taken by B for doing remaining 2/7 of work = (2/7) / {(X - 35) / 35X}
= 70X / 7(X - 35) = 10X / (X - 35) days
Therefore,
(5X/7) + {10X / (X - 35)} = 90 days (given)
Rearranging the equation we get,
5X(X-35) + 70X = 630 (X - 35)
Or 5 X^2 - 175X + 70X = 630X + 22050
Or X^2 - 147X + 4410 = 0
Solving for X,
(X - 105) (X - 42) = 0
It can be seen that X can not be 42.
So X must be 105 days.
Ans. A alone can finish the work in 105 days.
It can be shown that B alone can do the work in 52.5 days.
Verification:
A does 5/7 of work in (105*5/7) = 75 days.
B does the remaining work of 2/7 in (52.5*2/7) = 15 days.
So total number of days = 90