Time & Work
General Rules ( Work & Time )
1) If any work done by A in x day , then work done by A in one day = 1/x
2) If A's one day work = 1/x then A take x days to finish the work .
3)If A's working capacity is 2 time of B's working capacity then Ratio of work is 2 : 1 .
4) If ratio of worker in any work is 1 : 2 then worker will take time 2 : 1 .
5) If we increase or decrease quantity of time then work will increase or decrease .
6) If we increase number person in any work , then time to finish the work will decrease .
7) If we decrease number of person in any work , then time to finish the work will increase .
8) A and B take different time in any work then
work of A time taken of B
---------------- = -------------------------
work of B time taken of A
9) x person do any work in y days then one person do same work in xy days .
10) x person do any work in y days then z person take time in same work in xy/z
General Rules (Pipes & Cisterns )
1) If an inlet pipe can fill a cisterns in x hours , then the part filled in 1 hour = 1/x .
2) If an outlet pipe can empty a tank in y hours , then the part empties in 1 hour = 1/y .
3)If an inlet pipe can fill a tank in x hours and an outlet empties the full tank in y hours, then then the net part filled in 1 hour when both the pipes are opened
xy
= ---------
x - y
Rule 1
If A do any work in x days and B do same work in y days then together both will do that work in
xy
------------- days.
x + y
Example :
If Naman finish any work in 5days and sanam finish same work in 15 days . what time will they take to do the work ?
Sol.
Naman + Sanam do one work
5X15
= -----------------
5 + 15
= 75/20 = 15/4 = 3.75 days .
Rule 2
If A do any work in x days , B do same work in y days and C do same work in z days then together they will do that work in
xyz
------------------------- days.
xy + yz + zx
Example :
Rani do any work in 5 days , Madan do same work in 10 days and Amar do same work in 15 days .How many days will they finish it together .
Sol.
Rani + Madan + Amar work together
5X10X15
= --------------------------------- days
5X10 + 10X15 + 15X5
750
= -----------------------------------
50 + 150 + 75
= 750/275
=2.72 days .
Rule 3
A + B do any work in x days , B + C do any work in y days and C + A do any work in z days then
i) A + B + C do finish it in
2xyz
-------------------days
xy + yz + zx
ii) A finish whole work in
2xyz
-------------------------- days
xy + yz - zx
Example :
A + B do any work in 5 days , B + C do in 10 days and C + A do in 5 days . How many days will all three A + B + C finish it ?
Sol.
A + B + C do it
2X5X10X5
=-------------------------------days
5X10 + 10X5 + 5X5
= 500/125 = 4 days .
Problems on Pipes and Cisterns
Example :
1) Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. Find the time taken to fill the tank when both the pipes are turned on simultaneously.
Sol.
Both pipes together can fill the tank in
10X15
= ----------------
10 + 15
= 150/25 = 6 hours
2) Pipe A can fill a tank in 20 hours while pipe B alone can fill it in 30 hours and pipe C can empty the full tank in 40 hours . If all the pipes are opened together , how much time will be needed to make the tank full ?
Sol .
The tank will be full in
20X30X40
------------------------------------ hours
20X40 + 30X40 -20X30
= 24000/1400 =120/7 hours
Exercise
1) 24 men can complete a given job in 40 days. The number of men required to complete the job in 32 days, is
a)30 b)32 c) 34 d) 36
2)If a work can completed by Ain 30 days and by B in 60 days , then the number of days taken by them to finish the work , working together .
a) 20 b)25 c)45 d)50
Answer
1) a 2) a
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