P can do 1/2 of a work in 10 days and Q can do 1/5 of the same work in 4 days. In how many days can both finish the work, working together?

10 days

P = \(\frac{1}{2}\)W = 10 days = 20 days,

Q =  \(\frac{1}{5}\)W = 4 days = 20 days, 

Therefore the efficiency is same, i.e; P : Q = 1 : 1

⇒ Total work = 1 x 20 = 20 units.   ..(Efficiency × Days = Total work)

⇒ Time required by P + Q to complete the work = \(\frac{20}{1+1}\) =\(\frac{20}{2}\) = 10 days.   ..(\(\frac{Work}{Efficiency}\) = Time)