# Problems on Time required to Complete a Piece a Work

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 real-life 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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