Raju can finish a piece of work in 20 days. He worked at it for 5 days and then Jakob alone finished the remaining work in 15 days. In how many days can both finish it together?

10 days

Raju = 20 days,

Lets' take Raju's efficiency as 1.

Therefore, Total work = 1 x 20 days = 20 units,    ..(Efficiency × Days = Total work)

⇒ Raju worked for 5 days = 1 x 5 = 5 units,

⇒ Remaining work = 20 - 5 = 15 days,

⇒ Remaining work is completed by Jakob in 15 days = \(\frac{15}{Jakob}\) = 15 days,

⇒ Jakob = 1, (Efficiency)

⇒ Time required by Raju and Jakob to complete the work together = \(\frac{20}{1+1}\) = \(\frac{20}{2}\) = 10 days,  ..(\(\frac{Work}{Efficiency}\) = Time)