A can do a piece of work in 30 days and B in 12 days. They work together for 5 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work?
Answer & explanation
Correct answer: option 4
A : B
Days 30 : 12 = 2 : 5
Efficiency 5 : 2
Say, the total work = 60
Work done A + B in 8 days = Efficiency x No. Of Days = (2 + 5) x 5 = 7 x 5 = 35
Remaining work = 60 - 35 = 25
This work is completed by C in 10 days,
Thus efficiency of C = \(\frac{Work}{Days}\)
= \(\frac{25}{10}\) = 2.5
Time taken By C alone to complete this work = \(\frac{Total\; work}{Efficiency}\)
= \(\frac{60}{2.5}\) = 24 days