7. A takes 6 days less than the time taken by B to finish a piece of work. If both A and B
together can finish it in 4 days, find the time taken by B to finish the work.
Answers
Hey !
Given,
A takes 6 days less than the time taken by B to complete a piece of work.
Let the time taken by B to finish the work be x
=> time taken by A to finish the same work = x-6.
time taken by both working together = 4 days
In one day, calculate the part of work done.
Work done by A = 1/x
Work done by B = 1/(x-6)
Work done by both A and B, working together = 1/4.
Since, work done by both A and B is sum of their individual work done
=> 1/x + 1/(x-6) = 1/4
=> x-6/x(x-6) + x/x(x-6) = 1/4
=> (x-6+x)/x(x-6) = 1/4
=> 4(2x-6) = x²-6x
=> x²-14x + 24 = 0
=> x(x-2)-12(x-2) = 0
=> x = 12 and 2
If time taken by B is 2 days, A takes 2-6 = -4 (daysNon existence)
•°• If time taken by B is 12 days , A takes 12-6 = 6 days
•°• B takes 12 days to finish the work.
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