In an orchard, $\dfrac{1}{3}$ of the trees are guava trees, $\dfrac{1}{8}$ are banana trees and the rest are mango trees. If there are 117 mango trees in the orchard, how many trees in all are there?

Given,

Part of guava trees = $\dfrac{1}{3}$

Part of banana trees = $\dfrac{1}{8}$

Part of mango trees = 1 - (part of guava trees + part of banana trees)

$= 1 - \Big(\dfrac{1}{3} + \dfrac{1}{8}\Big) \\[1em] = 1 - \Big(\dfrac{8 + 3}{24}\Big) \\[1em] = 1 - \dfrac{11}{24} \\[1em] = \dfrac{24 - 11}{24} \\[1em] = \dfrac{13}{24}.$

No. of mango trees = Part of mango trees × Total number of trees

$117 = \dfrac{13}{24} \times \text{Total number of trees} \\[1em] \text{Total number of trees} = 117 \times \dfrac{24}{13} \\[1em] \text{Total number of trees} = 9 \times 24 = 216.$

Hence, total number of trees = 216.