Question

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

Answer 1

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  

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