A can do a piece of work in 24 days and B in 40 days. They work together for 12 days and then both leave the work. Then C alone finishes the remaining work in 6 days. In how many days will C finish the full work?
Answer & explanation
Correct answer: option 1
A : B
Days 24 : 40 = 3 : 5
Efficiency 5 : 3
Say, the total work = 120
Work done A + B in 8 days = Efficiency x No. Of Days = (3 + 5) x 12 = 8 x 12 = 96
Remaining work = 120 - 96 = 24
This work is completed by C in 6 days,
Thus efficiency of C = \(\frac{Work}{Days}\)
= \(\frac{24}{6}\) = 4
Time taken By C alone to complete this work = \(\frac{Total\; work}{Efficiency}\)
= \(\frac{120}{4}\) = 30 days