A garden has $$2000$$ trees, $$12\% $$ of these are mango trees, $$18\% $$ lemon trees and the rest are orange trees. Find the number of orange trees.

Question

Vedantu Content Team · Accepted Answer

Hint: Using the percentage of trees given, at first, we will find the number of mango and lemon trees in the garden. From them we can calculate the number of mango and lemon trees, then we will find the sum of the number of both trees and subtract it from the total number of trees to find the number of orange trees.Complete step-by-step answer: It is given that the total number of trees in the garden is $$2000$$.It is also given, $$12\% $$ of these are mango trees, $$18\% $$ lemon trees and the rest are orange trees.We have to find the number of orange trees in the garden. Given the total number of trees is $$2000$$.Also given $$12\% $$ of these are mango trees.So, the number of mango trees is found by using the percentage formula,Number of mango tree is $$12\%  \times 2000 = \dfrac{{12}}{{100}} \times 2000 = 240$$Hence there are $240$ mango trees in the garden.Also it is given in the garden there are $$18\% $$ lemon trees.So, the number of lemon trees is found using percentage formula,Number of lemon trees in the garden is $$18\%  \times 2000 = \dfrac{{18}}{{100}} \times 2000 = 360$$Hence there are $360$ lemon trees in the garden.Total number of mango and lemon trees are $$240 + 360 = 600$$It is given that the rest numbers are orange trees.Hence the number of orange trees is found by subtracting the number of lemon and mango trees from the total number of trees in the garden.Therefore, number of orange trees are $$2000 - 600 = 1400$$Hence, there are $$1400$$ orange trees in the garden.Note: The above problem can be written in one expression. That is,The number of orange trees are: $$2000 - (2000 \times 12\% ) - (2000 \times 18\% )$$Solving we get, $$2000 - 240 - 360 = 1400$$Hence the number of orange trees are$$1400$$.Also we can say in total $$100\% $$ of trees in the garden $$18 + 12 = 30\% $$ of trees are lemon and mango, then $$100 - 30 = 70\% $$ of trees are orange Hence $$70\%  \times 2000 = \dfrac{{70}}{{100}} \times 2000 = 1400$$ is the number of orange trees.

A garden has \[2000\] trees, \[12\% \] of these are mango trees, \[18\% \] lemon trees and the rest are orange trees. Find the number of orange trees.