In an orchard the number of apple trees are $\frac{1}{5}$ of the orchard, number of orange trees are $\frac{3}{13}$ of the orchard and the number of banana trees are 148 in number. What are the total number of trees in the orchard ?

Given :

Number of apple trees are $\frac{1}{5}$ of the orchard.

Number of orange trees are $\frac{3}{13}$ of the orchard.

Number of banana trees = 148.

To find :

We have to find the total number of trees.

Solution :

Let the total number of trees in the orchard be $x$.

This implies,

Number of apple trees =$\frac{1}{5}$ $x$

Number of orange trees = $\frac{3}{13}$ $x$

Number of banana trees =$ x-(\frac{1}{5} + \frac{3}{13})x $

=$ x(1 - \frac{13+15}{65}) $

= $x(1 - \frac{28}{65})$

$148 = x(\frac{65-28}{65})$

$148 = x(\frac{37}{65})$

$x = 148(\frac{65}{37})$

$x = 4(65)$

$x = 260$.

The total number of trees in the orchard is 260.

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