A alone can do a job in 30 days while B alone can do it in 45 days. A starts the job and after 5 days B joins him. After few more days, C joins them and they together finish the job. If C has done 16\(\frac{2}{3}\)% of the job, then in how many days was the job done?

17

⇒ C does 16\(\frac{2}{3}\)% = \(\frac{1}{6}\) of the work i.e 15

Then, A + B do 75 units of work

⇒ A alone does the work in 1st 5 days =  3 x 5 = 15

Remaining work (done by A and B together) = 75 - 15 = 60

⇒ A + B does the remaining work in =  \(\frac{60}{5}\) = 12 days

So,

The work completed in = 5 + 12 = 17 days