Key Points
Work is the job or task completed (Distance) in a specified time. Time and Work are in direct proportion. If the amount of work increases, time to complete the work also increases.
1)Work from Days:
If A can do a piece of work in n days, then A's 1 day's work = 1/ n
2)Days from Work:
If A's 1 day's work = 1 /n , then A can finish the work in n days.
3)Ratio:
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.
Work is the job or task completed (Distance) in a specified time. Time and Work are in direct proportion. If the amount of work increases, time to complete the work also increases.
1)Work from Days:
If A can do a piece of work in n days, then A's 1 day's work = 1/ n
2)Days from Work:
If A's 1 day's work = 1 /n , then A can finish the work in n days.
3)Ratio:
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.
Work as Man Days
Work=Man X Days
If a man does a work in 10 days, total work does is 10 man days. Two men will take 5 days (10 man days). The work done by one man in one day is 1/10th of total work.
Pipes and Cisterns
Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.
Outlet: A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet.
1.If an inlet pipe can fill a cistern in A hours, the part filled in 1 hour = 1/A (same principle as time and work).
2.If pipe A is ‘x’ times bigger than pipe B, then pipe A will take 1/xth (less time) of the time taken by pipe B to fill the cistern.
3.If an inlet pipe can fill a tank in A hours and an outlet pipe empties the full tank in B hours (B>A), then the net part filled in 1 hour when both the pipes are opened will be 1/A - 1/B.
4.If X and Y fill a cistern in m and n hours respectively, then together they will take (1/m + 1/n) hours to fill the cistern.
5.If an inlet pipe fills a cistern in a hours and takes x minutes longer to fill the cistern due to a leak in the cistern, then the time in which the leak will empty the cistern is given by a(1+a/x).
Outlet: A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet.
1.If an inlet pipe can fill a cistern in A hours, the part filled in 1 hour = 1/A (same principle as time and work).
2.If pipe A is ‘x’ times bigger than pipe B, then pipe A will take 1/xth (less time) of the time taken by pipe B to fill the cistern.
3.If an inlet pipe can fill a tank in A hours and an outlet pipe empties the full tank in B hours (B>A), then the net part filled in 1 hour when both the pipes are opened will be 1/A - 1/B.
4.If X and Y fill a cistern in m and n hours respectively, then together they will take (1/m + 1/n) hours to fill the cistern.
5.If an inlet pipe fills a cistern in a hours and takes x minutes longer to fill the cistern due to a leak in the cistern, then the time in which the leak will empty the cistern is given by a(1+a/x).
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