Raj alone can complete a work in 20 days and Pratap alone can complete the same work in half of the time taken by Raj. In how many days will both together complete 3/5  part of the total work ?

4 days

Efficiency ∝ $\frac{1}{time}$

                   Raj  :  Pratap

Time             20  :   10   = 2 : 1

Efficiency        1  :   2

Let the total work be 20 

total efficiency = 1 + 2 =3

$\frac{3}{5}$ of the work = 12 units

Time taken to complete this work = $\frac{work}{efficiency}$

                                                  = $\frac{12}{3}$ = 4days