Five technicians of a Studio A can do a work in 30 days. Eight technicians of a Studio B can do the same work in 15 days. In how many days can one technician of Studio A and one technician of Studio B, together do the same work?

$\frac{200}{3}$

According to the question,

5A x 30 = 8B x 15

5A = 4B

A : B = 4 : 5   (Efficiency)

⇒ Total work = 5(4) x 30 = 20 x 30 = 600 units,  ..(Efficiency × Days = Total work)

⇒ A + B can complete the work in = $\frac{600}{4 + 5}$ = $\frac{600}{9}$ = $\frac{200}{3}$ days.   ..($\frac{Work}{Efficiency}$ = Time)