Learn how to solve problems on time required to complete a piece a work when a person A completes a piece of work in n days, then work done by A in one days = 1/n th part of the work.
Now we will apply the above concept for solving some reallife problems to find the time required to complete the allotted work.
Solved problems on time required to complete a piece a work:
1. Anthony and Billy can built a wall in 6 days, Billy and Corey can do it in 9 days and Corey and Anthony in 12 days.
In how many days will they:
(i) finish together?
(ii) finish separately?
Solution:
(Anthony + Billy)’S 1 day work = 1/6
(Billy + Corey)’s 1 day work = 1/9
(Corey + Anthony) ‘s 1 day work = 1/12
[(Anthony + Billy) + (Billy + Corey) + (Corey + Anthony]‘s 1 day work = 1/6 + 1/9 + 1/12
(2 Anthony + 2 Billy + 2 Corey)‘s 1 day’s work = 12 + 8 + 6/72
2(Anthony + Billy + Corey)’s 1 day’s work = 26/72
Therefore, (Anthony + Billy + Corey)’s 1 day’s work = 26/72 × 2
Therefore, together Anthony, Billy, and Corey can complete the work in 72/13 = 5.5 days.
Therefore, Anthony’s 1 day’s work = (Anthony + Billy + Corey)’s 1 day’s work – (Billy + Corey)’s 1 day’s work
= 13/72 – 1/9
= (13 – 8)/ 72
= 5/72
Therefore, Anthony finishes the work in 72/5 days.
Billy’s 1 day’s work = (Anthony + Billy + Corey)’s 1 day’s work – (Corey – Anthony)’s 1 day’s work = 13/72 – 1/12
= (13 – 6)/72
= 7/72
Therefore, Billy finishes the work in 72/7 days.
Corey’s 1 day’s work = (Anthony + Billy + Corey)’s 1 day’s work – (Anthony + Billy)’s 1 day’s work = 13/72 – 1/6
= (13 – 12)/72
= 1/72
Corey can finish the work in 72 days.
2. Daniel can do piece of work in 15 days and Josh can do it in 10 days. They work together in 3 days, then Daniel goes away. In how many days will Josh finish the remaining work?
Solution:
Daniel’s 1 day’s work = 1/15
Josh’s day’s work = 1/10
(Daniel + Josh)’s 1 day’s work = 1/15 + 1/10 = 2 + 3/30 = 5/30 = 1/6
(Daniel + Josh)’s 3 day’s work = 1/6 × 3 = 1/2
Remaining work = (1 – 1/2) = (2 – 1)/2 = 1/2 which is to be done by Josh.
We know that, 1/10 work is done by Josh in 1 day.
1 work is done by Josh in 1/1/10 day = 1/1 × 10/1 = 10 days
1/2 work is done by Josh in 10 × 1/2 days = 5 days
Therefore, Josh will finish the remaining work in 5 days.
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