A and B can do certain work in 18 days and 30 days, respectively. They work together for 5 days. C alone completes the remaining work in 15 days. A and C together can complete $\frac{5}{6}$th part of the same work in:
Answer & explanation
Correct answer: option 3
A = 18 days,
B = 30 days,
⇒ A + B worked for 5 days = (5 + 3) x 5 = 40 units. (Efficiency × Days = Total work)
⇒ Remaining work = 90 - 40 = 50 units.
⇒ 50 units was completed by C in 15 days = \(\frac{50}{C}\) = 15 days
⇒ C = \(\frac{10}{3}\)
⇒ Time taken by A + C to complete \(\frac{5}{6}\)th work = 90 x \(\frac{5}{6}\) = 75 units,
⇒ \(\frac{75}{5 + 10/3}\) = 9 days. ..(\(\frac{Work}{Efficiency}\) = Time)