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HELLO! I am Jaspreet Kaur B.tech in Computer Science and Engineering ,Pantnagar University. Interests : Computer Programming, Engineering, Web Development Problem solving b https://unacademy.com/user/ jaspreet.kaur309-6837
Efficiency Efficiency is inversely proportional to the Time taken when the amount of work done is constant. Efficiency . Time Taken " The total work divided by the number of day will give us the work done in one day, which is also the capacity or the efficiency. Capacity/Efficiency Work done "1" day
Example : Mayank can finish a work in 10 days. Mahesh is 2 times as efficient as Mayank. If they work together, in hovw many days will the work be completed? Example 1 Solution Let us assume that Mayank complete 1 unit of work per day. Also, the total work-10 units. SO, Since Mahesh is two times as efficient as Mayank, then Mahesh can do 2 units of work per day.
Now, if they both work together, then the unit of work they can complete in one day equals one plus two i.e. three units. Therefore, the number of days taken by them together 10/3 days
Shortcut Shortcut: If A can finish a work in X days and B is K times as efficient as A, then the time required by both A and B working together to finish the job will be X/(1+K).
Example : Mayank can finish a work in 10 days. Mahesh is 2 times as efficient as Mayank. If they work together, in hovw many days will the work be completed? Example Solution Applying the direct shortcut Comparing with the formula we have X -10 and K-2. Therefore, the number of days taken by them together -10/3 days
Example : Rahul is three times as good a worker as Durgesh and takes 8 days less than Durgesh to finish the work; find the amount of time required by Rahul and Durgesh working together to do the job? Example 2 Solution: Let us assume that Rahul alone takes x days to complete the work. As we know, efficiency is inversely proportional to days, the number of days taken by Durgesh to complete the same work
Therefore, Rahul is taking 3x-x-2x days less than Durgesh; thus, 2x 8 or x 4 Hence we can say that Rahul and Durgesh alone take 4 and 12 days respectively to complete the work. Therefore together they will be taking 4 x 12/(4+12)-3 days.
Shortcut Shortcut: A is K times as good a worker as B, and takes X days less than B to finish the work. Then the amount of time required byA and B working together- KX/(K 2-1) days. 10
With Percentage Method Example : A is twice as efficient as B. if they take 6 days to finish a certain job together, how much Time will they individually take to complete the work? Solution : Using the percentage approach It is given that A is twice as efficient as B. If they are finishing the work in 6 days, then in one day they will do 100/6 % of worke. 16.66% as A is twice as efficient, work done by A in one day will be twice the work done by B 12
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