# 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.

$\par&space;A's&space;one&space;day's&space;work&space;=$  $\frac{1}{10}$

$\par&space;B's&space;one&space;day's&space;work$ $=&space;\frac{1}{15}$

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

$\par&space;So,&space;both&space;together&space;will&space;finish&space;the&space;work&space;in&space;6&space;days.$

$\par&space;\underline{Shortcut&space;method}$

$\frac{10&space;\times&space;15}{10&space;+&space;15}&space;=&space;\frac{150}{25}&space;=&space;6$