Question

10] The ratio of number of mango trees to chikoo trees in an orchard is 5: 7. If 40 more trees of each type are planted the ratio of trees would be 25:31. Then find the number of mango and chikoo trees in the orchard.​

Answer 1

Given :

• The ratio of number of mango trees to chikoo trees in an orchard is 5: 7.
• If 40 more trees of each type are planted the ratio of trees would be 25:31.

To Find :

• Number of Mango and Chikoo Trees .

Solution :

$\longmapsto\tt{Let\:Mango\:trees\:be=5x}$

$\longmapsto\tt{Let\:Chikoo\:trees\:be=7x}$

Now ,

• If 40 more trees of each type are planted the ratio of trees would be 25:31.

$\longmapsto\tt{Mango\:Trees=5x+40}$

$\longmapsto\tt{Chikoo\:Trees=7x+40}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+40}{7x+40}=\dfrac{25}{31}}$

$\longmapsto\tt{31(5x+40)=25(7x+40)}$

$\longmapsto\tt{155x+1240=175x+1000}$

$\longmapsto\tt{155x-175x=1000-1240}$

$\longmapsto\tt{-20x=-240}$

$\longmapsto\tt{x=\cancel\dfrac{-240}{20}}$

$\longmapsto\tt\bf{x=12}$

Value of x is 12 .

Therefore :

$\longmapsto\tt{No.\:of\:Mango\:Trees=5(12)}$

$\longmapsto\tt\bf{60\:Trees}$

$\longmapsto\tt{No.\:of\:Chikoo\:Trees=7(12)}$

$\longmapsto\tt\bf{84\:Trees}$

Answer 2

Given

• The ratio of number of mango trees to chikoo trees in an orchard is 5: 7.
• If 40 more trees of each type are planted the ratio of trees would be 25:31.

To find

• The number of mango and chikoo trees in the orchard.

Solution

• Let the ratio be x.

$\sf\pink{⟶}$ Number of mango trees = 5x

$\sf\pink{⟶}$ Number of chikoo trees = 7x

• If 40 more trees of each type are planted the ratio of trees would be 25:31.

$\sf\pink{⟶}$ Number of mango trees = 5x + 40

$\sf\pink{⟶}$ Number of chikoo trees = 7x + 40

⠀

According to the question

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{5x + 40}{7x + 40} = \dfrac{25}{31}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {31(5x + 40) = 25(7x + 40)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {155x + 1240 = 175x + 1000}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {175x - 155x = 1240 - 1000}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {20x = 240}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \cancel{\dfrac{240}{20}}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = 12}$

⠀

Therefore,

$\sf\pink{⟶}$ Number of mango trees = 5 × 12

• Number of mango trees = 60

$\sf\pink{⟶}$ Number of chikoo trees = 7 × 12

• Number of chikoo trees = 84

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬