Methods to solveC problems on Time n Work
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Example : Arun, Barun and Tarun can do a work alone in 10, 12 and 15 days respectively. If all three work together then in how many days does the job get completed? Solution LCM of 10,12 and 15 60 LCM Method Assume that the total work is of 60 units. Amount of work done by Arun in one day - 60/106 units per day. Similarly, the amount of work done by Barun in one day 60/12-, 5 units per day.
And the amount of work done by Tarun is 60/15 4 units per day. So if all three together work then thee amount of work done in one day 65+ 4 15 units per day Therefore, the number of days required to complete the work60/15 4 days.
Shortcut Shortcut: If two people take X and Y days respectively to complete a work alone, then together they will complete it in XxY/(X+Y) days
Example : Arun, Barun and Tarun can do a work alone in 10, 12 and 15 days respectively. If all three work together then in how many days does the job get completed? Solution The number of days required to complete the work 10 x 12 x 15/(120 180 +150) LCM Method 1800/450 4 days
Example : Rahim can finish a work in 10 days and Ram can finish the same work in 40 days. If Ram and Rahim both work together then what is the total number of days taken? Solution Fraction Method Ram can finish the work in 10 days i.e. in one day he will do 1/10th of the work. Rahim can finish the work in 40 days i.e. in one day he will do 1/40th of the work. So, in one day, both working together can finish - (1/10) (1/40)5/40 1/8th of the work.
"Problem : Ravi can do a job in 10 days. Percentage Method Raman can do the same job in 20 days. They together start doing the job but after 4 days Raman leaves. How many more days will be required by Ravi to complete this job alone? " Solution: Ravi can finish a job in 10 days i.e in one day he can finish 10 % of the job. Raman can finish the same job in 20 days i.e. in one day he can finish 5 % of the job. So, working together, in a day they can do 10 5 -15 % of the job.
In the 4 days, if they worked together, they would have finished 4 15% 60% of the job. Percentage Method So, job left-: 100-60 40%. This work has to be done by Ravi who does 10 % of the job in a day. So, to finish the remaining 40%, he will take 40/ 10 4 more days.
Example : A Cistern has three pipes A, B, and C. Pipe A can fill a Cistern in 10 hrs, Pipe B can fill a Cistern in 5 hrs while Pipe C can empty the Cistern in 20 hrs. If they are switched on at the same Time; in how many hours will the Cistern be filled? Negative Work Solution: In one hour Pipe A can fill 100/10= 10% of the Cistern. In one hour Pipe B can fill 100/5-20 % of the Cistern. In one hour Pipe C can empty 100/20-5 % of the Cistern. 10
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Graduated from Pantnagar University , Computer Science Engineer , Web Developer , Programmer , Cleared CAT Examination