A alone can do a piece of work in 20 days. B alone can do \(\frac{3}{4}\) of the same work in 9 days and C alone can do \(\frac{1}{2}\) of the same work in 15 days. They started the work and after some days A left the job and if they got Rs. 30000 for the whole work and C get Rs. 5000 more than A. Find after how many days A left the work?

\(\frac{5}{3}\) days

A can do a piece of work in = 20 days

B can do a piece of work in = 9 × \(\frac{4}{3}\) = 12 days

C can do a piece of work in = 15 × \(\frac{2}{1}\) = 30 days

Let A worked for x days and (B+C) for y days and they got Rs. 30000 in total

Hence

60 unit= 30000

1 unit    =    500 

  ↓ x5           ↓ x5

5 unit          2500

( C got Rs.5000 more than A so he worked 5 unit more than A)

3 x + 11 y = 60 ------ (i)

2 y -  3 x = 5 ------- (ii)

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        13 y = 65

            y = 5     ⇒ x = \(\frac{5}{3}\) days