Question

In an orchard, 1/3 of the trees are guava trees, 1/8 are banana trees and the rest are mango trees. If there are 117 mango trees in the orchard, how many trees are there in all? Please give explanation.

Answer 1

let total number of trees be x.
no.of guava trees=1/3x.
no.of mango trees=1/8x.
remaining trees=x-(1/3x+1/8x)
ATQ
x-(1/3x+1/8x)=117
x-(8x+3x/24)=117
x-(11x/24)=117
24x-11x/24=117
13x/24=117
13x=117×24
x=117×24/13
x=216
therefore total no.of trees =216

Answer 2

Given :

• Guava Trees = 1/3
• Banana Trees = 1/8
• Mango trees = 117

To find :

The trees in all.

Solution :

Adding, guava and banana trees:

$\dfrac{1}{3} + \dfrac{1}{8}$

• LCM of 3 and 8 is 24

$\dfrac{8 + 3}{24}$

$\dfrac{11}{24}$

So,

• Guava and banana trees are 11/24

Finding mango trees :

$\dfrac{24}{24} - \dfrac{11}{24} = \dfrac{13}{24}$

• Mango trees are = 13/24

Given mango trees are 117

Finding total trees :

$117 \times \dfrac{24}{13} = 216$

Hence, The total number of trees in the orchard are 216.