To calculate work done in a given time in general if a person A completes a piece of work in a ‘n’ days, then A’s one day work = 1/n.
If a man takes 10 days to complete a piece of work, then according to the unitary method work done in one day = 1/10.
Now we will apply the concept of solving some real-life problems to find the work done in a given period of time.
Solved examples to calculate work done in a given time:
1. Adam can do a piece of work in 15 days and Brandon can finish it in 10 days. They work together for 5 days and then Adam goes away. In how many days will Brandon finish the remaining work?
Solution:
Adam can finish the work in 15 days.
Therefore, Adam’s 1 day’s work = 1/15
Brandon can finish the work in 10 days.
Therefore, Brandon’s 1 day’s work = 1/10
So, (Adam + Brandon)‘s 1 day’s work = 1/15 + 1/10 = (2 + 3)/30 = 5/30 = 1/6
Therefore, (Adam + Brandon)‘s 5 day’s work = 5 × 1/6 = 5/6
Remaining work = 1 – 5/6 = 6-5/6 = 1/6
This remaining work has to be done by Brandon.
Complete work is done by Brandon in 10 days.
Therefore, 1/6 of the work is done by Brandon in (10 × 1/6) days = 5/3 days.
Hence, the remaining work is done by Brandon in 5/3 days.
2. Alex can do 3/4 of the work in 12 days and Ben can do 1/8 th of the work in 2 days. In how many days both Alex and Ben can together do the work?
Solution:
3/4 of the work is done by Alex is 12 days.
Therefore, the whole work will be done Alex in 12 × 4/3days = 16 days.
Therefore, Alex’s day’s work = 1/16
Similarly, 1/8 of the work is done by Ben in 2 days.
Therefore, the whole work will be done Ben in 2 × 8/1 = 16 days
So, Ben’s 1 day work = 1/16
Now (Alex + Ben)’s 1 day’s work = 1/16 + 1/16 = 2/16 = 1/8
Therefore, (Alex + Ben) together will complete the work in 8 days.
More problems to calculate work done in a given time:
3. Nancy can embroider a dress in 15 hours while Sam can do the same in 10 hours. Working together how much time will they take to embroider 5 dresses?
How many dresses will be embroidered in 54 hours?
Solution:
Nancy can embroider a dress in 15 hours.
So, Nancy’s 1 hour work = 1/15
Also, Sam can embroider a dress in 10 hours.
So, Sam’s 1 hour work 1/10
Nancy’s and Sam’s 1 hour work = 1/15 + 1/10 = 2+3/30 = 5/30 = 1/6
So, they will together take 6 hours to embroider 1 dress.
So, working together, time taken to embroider 1 dress = 6 hours.
Therefore, time taken to embroider 5 dresses = (6 × 5) hours = 30 hours.
Also, number of dresses embroidered in 6 hour = 1
Number of dresses embroidered in 1 hour = 1/6
Therefore, number of dresses embroidered in 54 hours = 1/6 × 54 = 9
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