A does a work in 10 days and B does the same work in 15 Days. In how many days they together will do the same work.

\par A's one day's work =  \frac{1}{10}

\par B's one day's work = \frac{1}{15}

\par (A + B)'s one days work = \left [ \frac{1}{10}+\frac{1}{15} \right ]  = \frac{1}{6}

\par So, both together will finish the work in 6 days.

\par \underline{Shortcut method}

\frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6