A can complete one-third of a work in 5 days and B can do $\frac{2}{5}$th of the same work in 10 days. They work together for 6 days. The remaining work is completed by C in 18 days. C alone will do the same work in:
Answer & explanation
Correct answer: option 1
A = \(\frac{1}{3}\)W = 5 days = 15 days,
B = \(\frac{2}{5}\)W = 10 days = 25 days,
⇒ A + B worked for 6 days = (5 + 3) x 6 = 8 x 6 = 48 units, ..(Efficiency × Days = Total work)
⇒ Remaining work = 75 - 48 = 27 units,
⇒ C completes the remaining work in 18 days = \(\frac{27}{C}\) = 18 days,
⇒ C = \(\frac{27}{18}\) = \(\frac{3}{2}\) (Efficiency)
⇒ Time required by C to complete the work alone = \(\frac{75}{3/2}\) = 50 days, ..(\(\frac{Work}{Efficiency}\) = Time)