in an orchard there are $\frac{1}{8}$ lemon trees, $\frac{1}{3}$ mango trees and rest are banana trees. if there are 117 banana trees how many trees are there in total?

Let us assume that total number of trees in the orchard are x.
So,
the lemon trees will be $\left(\frac{1}{8}\right)\ast x=\frac{x}{8}$
the mango trees will be $\left(\frac{1}{3}\right)\ast x=\frac{x}{3}$
The remaining trees are the banana trees.
Banana trees $=x-\left(\frac{x}{8}\right)-\left(\frac{x}{3}\right)=\left(\frac{13}{24}\right)\ast x$
we are given that banana trees = 117
Banana Trees are
$\left(\frac{13}{24}\right)\ast x=117$
$x=\frac{(117\ast 24)}{13}$
therefore, x = 216
Hence, the total number of trees are 216.