Work, Profit & Loss
Calculus
Level
2
A does 80% a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work ?
38
40
37.5
37
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First of all, this isn't a calculus question. The way I approach this is to first find out what is A's work(labor) rate, meaning how much can A do ( in %) per day. We are told that A does 80% in 20 days. Hence, it is short of saying A can do 4% of the work (total work = 100%) in 1 day. It also means that A will finish the work (100%) in 25 days. TOGETHER ( A+B), they both can finish the remaining work that would have taken A 5 days to do in 3 days instead. This means that their combined effort results in doing the remaining 5 days work (100%) in 3 days = 60% (which is 3/5). So if they both started working together, the 25 day job for A will now be a 15 day job for A and B (which is 60% of 25). This means that their combined work effort per day of the total is 6.666% per day. Since we know that by himself A work effort per day = 4% we can now calculate B's work effort per day as 6.66-4 = 2.666%. Using this we can then calculate the number of days if B worked by himself to be 100/2.666 = 37.5 days.