Question

If in an orchard , 1/6 are orange trees, 2/9 are mango trees and the rest are banana trees. if the no of banana trees are 165, find the total number of trees in the orchard.

Answer 1

Answer:

270 trees

Step-by-step explanation:

Let the total number of trees be $x$

Given,

$\frac{1}{6}\ of\ the\ total\ trees\ are\ orange\ trees$

⇒ Orange trees $=\frac{1}{6}x$

$\frac{2}{9}\ of\ the\ total\ trees\ are\ mango\ trees$

⇒ Mango trees $= \frac{2}{9}x$

$Remaining\ are\ banana\ trees$

⇒ Banana trees = $x - (\frac{1}{6}x\ +\ \frac{2}{9} x)\ =\ x\ - (\frac{3x\ + \ 4x}{18} )$

                          $= x\ -\ \frac{7x}{18}\ =\ \frac{18x\ - \ 7x}{18}\ = \frac{11x}{18}$

Given,

  Number of Banana trees = 165

                                      $\frac{11x}{18} = 165$

                                       $x = \frac{165*18}{11} = 15*18$

                                      $x = 270$

   

Therefore,

The total number of trees = $x$ = 270 trees

Hope this helps.

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