Question

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?

Answer 1

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.