A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 days. In how many days both A and B together can do the work?

A can do 1/3 work $=5$ days
A can do the whole work $=5\times 3=15$days
B can do 2/5 of the work $=10$ days
B can do the whole work $=10\times 5/2=25$ days.
Let total work is 75 unit (LCM of 15 and 25).
${}_{\mathrm{B}-25}{}^{\mathrm{A}-15}>75{<}_{3 \mathrm{unit}/\mathrm{day}}^{5 \mathrm{unit}/ \mathrm{day}}$
Both A and B together can do the whole work

$=75/(5+3)=9.37$ days