Raju can do a piece of work in 10 days

Asked by admin @ 04/08/2021 in Math viewed by 342 People

raju can do a piece of work in 10 days,vicky in 12 days,tinku in 15 days.they all started work together,but raju leaves afte 2 days,vicky leaves 3 days before the work is completed. in how many work is completed

Answered by admin @ 04/08/2021

Given,

Raju can do a piece of work in 10 day.

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

Similarly,

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

Tinku 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 Raju in 2 days = 2/10

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

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

Work done by tinku in x days = x/15

Now, Total work = 1

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

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