Question

A can do a piece of work in 15 days. B can do the same work in 12 days and C can

finish the same piece of work in 20 days. They started the work together for 2 days
and then B and C leaves. In how many days will A finish the remaining work?​

Answer 1

9 days

Explanation:

A does in 15days, so A in 1day does 1/15part

B does in 12days, so B in 1day does 1/12part

C does in 20days, so C in 1day does 1/20part

So. A+B+C in 1 day-- 1/15+1/12+1/20=(4+5+3)/60= 12/60=1/5 and in 2days 2/5 part..hence remaining work=1/1–2/5=(5–2) =3/5part.

Now A in 1/15 part takes 1day

So, in 3/5 part 15×3/5 = 9 days.

Answer 2

`9\ days`

Explanation:

`We\ are\ given:\\No.\ of\ days\ A\ takes\ to\ complete\ some\ amount\ of\ work=15\ days\\No.\ of\ days\ B\ takes\ to\ complete\ the\ same\ amount\ of\ work=12\ days\\No.\ of\ days\ C\ takes\ to\ complete\ the\ same\ amount\ of\ work\ as\ A\ and\ B\ =20\ days\\`

`Now,\\We\ can\ say\ that\ an\ object\ has\ to\ complete\ (1)/(n)th\ of\ the\\ work\ daily,\ to\ complete\ the\ work\ in\ n\ number\ of\ days.\ This\ is\ however\\ only\ true\ if\ the\ object\ covers\ equal\ amounts\ of\ work\ each\ day.`

`Here,\\In\ 1\ day,\\A\ would\ cover\ (1)/(15)th\ of\ the\ work.\\B\ would\ cover\ (1)/(12)th\ of\ the\ work.\\C\ would\ cover\ (1)/(20)th\ of\ the\ work.`

`Now,\\We\ are\ also\ given\ that:\\They\ work\ together\ for\ 2\ days\ on\ the\ same\ work.\\Hence,\\Total\ work\ done\ in\ 1\ day\ by\ A,B\ and\ C=(1)/(15)+(1)/(12)+(1)/(20)=(4+5+3)/(60)=(12)/(60)=(1)/(5)\\Hence, Total\ work\ done\ in\ 2\ days\ by\ A,B\ and\ C=2*(1)/(5)=(2)/(5)`

`Hence,\\The\ portion\ of\ the\ total\ work\ left=1-(2)/(5)=(5-2)/(5)=(3)/(5)\\So,\\Since\ A\ has\ to\ complete\ (3)/(5)th\ of\ the\ work,\ lets\ compute\ the\ no.\ of\ days\ it\ takes\ to\ do\ so.\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ the\ entire\ work=15\ days\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ (3)/(5)th\ of\ the\ entire\ work=15*(3)/(5)=9\ days`