In an orchard, $\frac{1}{3}$ of the trees are guava trees, $\frac{1}{8}$ 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 ?

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Solution

Let there are n trees in an orchid
Given $\frac{1}{3}$ of the trees are guava and $\frac{1}{8}$ of the trees are banana
Remaining are Mango i.e.,
$n - \frac{n}{3} - \frac{n}{8} =$ Mango trees
Given Mango trees $= 117$
$117 = \frac{24 n - 8 n - 3 n}{24}$
$117 = \frac{13 n}{24}$
$n = 9 \times 24$
$n = 216$
There are $216$ trees in the orchid.

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In an orchard, 13 of the trees are guava trees, 18 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 ?

Let there are n trees in an orchidGiven 13 of the trees are guava and 18 of the trees are bananaRemaining are Mango i.e.,n−n3−n8= Mango treesGiven Mango trees =117117=24n−8n−3n24117=13n24n=9×24n=216There are 216 trees in the orchid.

In an orchard, $\frac{1}{3}$ of the trees are guava trees, $\frac{1}{8}$ 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 ?