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 ?

if x and y are no of days taken by A and B respectively then 

work done by A and B = $$\frac{1}{x}$$+$$\frac{1}{y}$$

total time taken = $$\frac{x+y}{xy}$$

work done by 1 technician of studio A in 1 day = $$\frac{1}{30 \times 5}$$

work done by 1 technician of studio B in 1 day = $$\frac{1}{15 \times 8}$$

time taken to complete the work together = $$\frac{1}{30 \times 5}$$ + $$\frac{1}{15 \times 8}$$ = $$\frac{200}{3}$$