A can complete a work in 20 days. while B can complete the same work in 25 days. Both worked together for 10 days and then C alone completed the remaining work in 10 days. In how many days will A, B and C together complete the same work?

10 days

A = 20 days, B = 25 days,

⇒ A + B worked for 10 days = (5 + 4) x 10 = 9 x 10 = 90 units,   ..(Efficiency × Days = Total work)

⇒ Remaining work = 100 - 90 = 10 units,

⇒ Remaining work is completed by C in 10 days = \(\frac{10}{C}\) = 10 days,

⇒ C = 1, (Efficiency)

⇒ Time required by A + B + C to complete total work = \(\frac{100}{5+4+1}\) = \(\frac{100}{10}\) = 10 days,     ..(\(\frac{Work}{Efficiency}\) = Time)