Question

Raman can do a piece of work in half the time taken by kapil. sunil can do the same work in one-third of the time taken by raman. all three of them work on it for 30 days after which kapil leaves. sunil and raman complete the remaining work in 18 more days. how many days would it take for raman alone to complete the total work

Answer 1

let say in 1 day kapil can do x unit of work     --------------------------(1)

time required by raman to complete x unit of work = 1/2 days

so in 1/2 day raman can do x unit of work

so in (1/2 × 2) = 1 days raman can do 2 × x = 2x unit of work    -------------(2)

sunil can do 2x unit of work in 1/3 days ( that is one third of time taken by raman)

so in 1/3 days sunil can do 2x unit of work

so in ( 1/3 × 3) = 1 days sunil can do 2x × 3 = 6x unit of work.    ----------------(3)

so by adding 1 , 2 and 3 , we get unit of work done if three works together in one day.

⇒  work done by Raman , kapil  and sunil in 1 day = x + 2x + 6x = 9x

⇒ work done by raman , kapil and sunil in 30 days = 30 × 9x = 180x

  After 30 days , kapil left ,

  so work done by raman and sunil in 1 day = 2x + 6x = 8x

so work done by raman and sunil in 18 days = 18 × 8x = 144x

Total work is ( work done by three in 30 days + work done by Raman and Sunil in           18 days)

so Total Work = 180x + 144x = 324x

number of days required by raman to complete work alone

   = total work/work done by raman in 1 day = 324x/2x = 162 days

so Raman would have taken 162 days to complete work alone.