Question

George can do a piece of work in 10 days, paul in 12 days and hari in 15 days. they all start the work together, but george leaves after 2 days and paul leaves 3 days before the work is completed. in how many days is the work completed?

Answer 1

Given,

George can do  a piece of work in 10 day.

So,George can  do 1/10 piece  of  work in 1 day

Similarly,

Paul   can  do 1/12  piece  of work in 1  day

Hari can  do  1/15 piece of  work in  1  day

Now, Let the work will be  complete in x  days as  per  given conditions.

Firstly, work done  by George  in  2 days  = 2/10

Since  paul  leaves  before  3  days  of  work completed , Therefore, He has  worked  for   (x-3) days

Work done by  paul by in  (x-3) days = (x-3)/12

Work done by  hari in  x  days = x/15

Now, Total work = 1

$\frac{2}{10}+\frac{x-3}{12}+\frac{x}{15}=1\\\;\\\frac{1}{5}+\frac{5x-15+4x}{60}=1\\\;\\\frac{9x-15}{60}=1-\frac{1}5}\\\;\\\frac{9x-15}{60}=\frac{4}{5}\\\;\\\frac{9x-15}{12}=4\\\;\\9x-15=48\\\;\\9x=63\\\;\\x=7$

Answer 2

George can do a piece in 10 days

⇒ 1 day = 1/10 of the work

Paul can do a piece in 12 days

⇒ 1 day = 1/12 of the work

Hari can do a piece in 15 days

⇒ 1 day = 1/15 of the work

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Amount of work completed by George, Paul and Hari in 2 days:

1 day = 1/10 + 1/12 + 1/15 = 1/4

2 days = 1/4 x 2 = 1/2 of the work

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Amount of work completed by Hari alone in the last 3 days:

1 day = 1/15

3 days = 3/15 = 1/5 of the work

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Amount of work remaining:

1 - 1/2 - 1/5 = 3/10

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Let the number of days Paul work be x

Amount of work completed by Paul and Hari in x days:

1 day = 1/12 + 1/15 = 3/20

x days = 3x/20 of the work

Solve x:

3x/20 = 3/10

30x = 60

x = 2

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Find the total number of days needed:

Total number of days = 2 + 3 + 2 =  7

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Answer: The work is completed in 7 days

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