Question

in an orchard ,40% are lichi trees,32%are mango trees and the rest are guava trees.if there are 105 guava trees,find the number of lichi and mango trees.

Answer 1

Let the number of trees in an orchard be x

Number of lichi trees = 40% of trees in orchard = 40% of x = 40/100 × x = 40x/100

Number of mango trees = 32% of trees in orchard = 32% of x = 32/100 × x = 32x/100

Number of guava trees = 105

Number of trees - (Number of lichi + Number of mango trees) = Number of guava trees

So, equation formed :

$\tt{x - ( \frac{40x}{100} + \frac{32x}{100}) = 105 }$

$\tt{x - \frac{40x}{100} - \frac{32x}{100} = 105}$

$\tt{x - \frac{72x}{100} = 105}$

$\tt{\frac{x \times 100}{1 \times 100} - \frac{72x}{100} = 105}$

$\tt{ \frac{100x}{100} - \frac{72x}{100} = 105}$

$\tt{\frac{28x}{100} = 105}$

$\tt{28x = 105 \times 100}$

$\tt{28x = 10500}$

$\tt{x = \frac{10500}{28}}$

$\tt{x = 375}$

Number of lichi trees = 40x/100 = 40(375)/100 = 15000/100 = 150

Number of mango trees = 32x/100 = 32(375)/100 = 12000/100 = 120

Therefore number of lichi trees in orchard are 150 and number of mango trees are 120.