Work and Time problems, time and work shortcut trick to solve problems quickly.

Work and Time problems:

Work and Time Problems :

Rules :

1) Keep the unknown number right and all the remaining numbers left.

2) If a man does a work in 5 days, then his work of one day = 1 / 5.

3) If a man's one - day work is 1 / 5 , then the total work will be finished in 5 days.

4) Work is compared by understanding the work of one man each day.

5) If the answer is to come in excess, then multiply by the left and right numbers. if the answer is to come in low, then divide by the left and right number.

Examples :

1) It takes a person 10 days to complete a task. If it takes another 15 days for the other to do the same work, how many days will it take for both of them to complete the work?

Ans. :

Days of both = ( Multiplication of two numbers ) / ( The sum of two numbers )

Days of both = ( 10 × 15 ) / ( 10 + 15 )

                         = 150 / 25 

                         = 6 days.

2) It takes a person 20 days to complete a task. If it takes another 30 days for the other to do the same work, how many days will it take for both of them to complete the work?
Ans. :
Days of both = ( Multiplication of two numbers ) / ( The sum of two numbers )
Days of both = ( 20 × 30 ) / ( 20 + 30 )
                         = 600 / 50
                         = 12 days.

3) It takes Ram and Sham 20 days to do a job. If Ram alone does the same work in 30 days, how many days will Sham do the same work in the evening alone?
Ans. :
Days alone = multiplication / difference
                     = ( 20 × 30 ) / ( 30 - 20 )
                     = 600 / 10
                     = 60.
Therefore, Sham takes 60 days to complete the same work.

4) It takes Ram and Sham 4 days to do a job. If Ram alone does the same work in 6 days, how many days will Sham do the same work in the evening alone?
Ans. :
 Days alone = multiplication / difference
                     = ( 4 × 6 ) / ( 6 - 4 )
                     = 24 / 2
                     = 12.
Therefore, Sham takes 12 days to complete the same work.

5) It takes 10 days for Ram to do one job, 20 days for Hari and 30 days for Ganesh. So how many days will it take for all three to complete the work?
Ans. :
= 10,  b = 20,  C = 30.
Day for Three = ( a × b × c ) / ( ab + bc + ac )
Days for Three = ( 10 × 20 × 30 ) / { ( 10 × 20 ) + ( 20 × 30 ) + ( 30 × 10 ) }
= ( 10 × 20 × 30 ) / 200 + 600 + 300 )
Days for Three = 6000 / 1100.
                            = 60 / 11
                            = 5.4 5 days

6) Both Ram and Hari do the same work in 10 days, Hari and Ganesh in 12 days, Ganesh and Ram in 15 days, while the three together will complete the work in how many days.
Ans. :
a = 10,   b = 12,   c = 15
Days for Three = ( 2 × a × b × c ) / ( ab + bc + ac )
= ( 2 × 10 × 12 × 15 ) / { ( 10 × 12 ) + ( 12 × 15 ) + ( 10 × 15 )
= 3600 / ( 120 + 180 + 150 )
= 3600 / 450
= 8 days.

7) A completes a task in 80 days. But after working for 10 days, A left. And B completed the remaining work in 35 days, while B alone completed the work in how many days.
Ans. :
a = 80,  b = 10,  c = 35.
Days = ( ac ) / ( a - b )
          = ( 80 × 35 ) / ( 80 - 10 )
          =  2800 / 70
          = 40 Days.
Therefore, B takes 40 days to complete the same work.

8) A works at twice the speed of B. It takes 18 days for both of them to work together. So A alone will complete the work in how many days.
Ans. :
Suppose, twice speed = n = 2.
Days = m = 18.
A days to work = { ( n + 1 ) / n } × m
                            = { ( 2 + 1 ) / 2 } × 18
                            = 27 days.

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