N can do a piece of work in 80 days. He works at for 10 fdays and then M alone finishes the remaining work in 42 days. In how much time will N and M, working together , finish the work?
Let's first find out how much work N can do in a day:
N can do the work in 80 days, so in one day, N can complete 1/80th of the work.
Now, N works for 10 days, so the amount of work completed by N in 10 days is (1/80) * 10 = 1/8th of the work.
The remaining work is (1 - 1/8) = 7/8th of the total work.
M alone completes the remaining 7/8th of the work in 42 days. Let M's daily work rate be represented as M's work in one day.
M's work in one day = (7/8) / 42 = 7 / (8 * 42) = 7 / 336 = 1/48
Now, let's find the combined work rate of N and M when they work together. The combined work rate is the sum of their individual work rates.
(N + M)'s work in one day = (1/80) + (1/48)
Now, let's calculate their combined work rate:
(N + M)'s work in one day = (1/80) + (1/48) = (3/240) + (5/240) = 8/240 = 1/30
Now that we know their combined work rate is 1/30, we can find out how many days it will take them to complete the whole work together.
Let D be the number of days required for N and M together to finish the work.
Using the formula: Work = Rate × Time, we have:
1 (the whole work) = (1/30) × D
Now, solve for D:
D = 1 / (1/30) = 30 days
So, N and M, working together, will finish the work in 30 days.
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