A can do a piece of work in 60 days, which B can do in 40 days. Both started the work but A left 10 days before the completion of the work. The work was finished in how many days?
Answers
Answer:
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Step-by-step explanation:
A left the job 10 days before the completion.
So, B worked alone for the last 10 days.
First,
we will calculate B’s 10 days work,
which he did alone.
In 10 days B will do 10 × 1/40 = 1/4th of the work.
Remaining work 1 - ¼ = ¾ (Which A and B have done together).
A and B can do 1/60 + 1/40 work in 1 day.
Their one-day’s work is 1/60 + 1/40 = (2 + 3)/120 = 5/120 = 1/24.
They can finish the work in 24 days.
They would have done three-fourth of the work in 24 × 3/4 = 18 days
.
⇒ Total days = 18 + 10 = 28.
A's 1 day work = 1/60
B's 1 day work = 1/40
Together they can finish in = 1/60 + 1/40 = 1/24
Therefore, together they take 24 days to complete the work.
Now, if A left 10 days before completion then,
Number of days A & B worked together = 24-10 = 14 days.
Percent completion of both A & B working together for 14 days is,
(1/24) × 14 × 100 = 58.33%
B's 1 day efficiency = 1/40 ×100 = 2.5%
& the left work is = 100 - 58.33 = 41.67%
Therefore, no. of days further B will take to complete the work is,
41.67/2.5 = 16.67 days
Therefore, the work finished at 14+16.67 = 30.67 days.
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