Question

the ratio of number of trees to chickoo trees in an orchard is 2:3 .if 5 more trees of each type of are planted the ratio of trees would be 5:7 .then find the number of mango and chickoo trees in the orchard .?​

Answer 1

Question:

The ratio of number mango of trees to chickoo trees in an orchard is 2 : 3. If 5 more trees are added to each ratio it's becomes 5 : 7

Find the number of mango and chickoo trees in the orchard.

Answer:

• Mango trees = 20
• Chickoo trees =30

Explanation:

Let's assume the common ratio as $\boldsymbol x$

• Number of mango trees = $2x$
• Numer of chickoo trees = $3x$

Adding 5 more trees to each.

New number of,

• Mango trees = $(2x + 5)$
• Chickoo trees = $(3x + 5)$

According to the question,

$\implies \: (2x + 5) : (3x + 5) = 5 : 7$

Solving for $\boldsymbol x$

$\implies \: \dfrac{(2x + 5)}{(3x + 5)} = \dfrac{5}{7}$

$\implies \: 7(2x + 5) = 5(3x + 5)$

$\implies \: 14x + 35 = 15x + 25$

$\implies \: 35 - 25 = 15x - 14x$

$\implies \: x = 10$

Hence, number of :-

• Mango trees = $2x = \bf 20$
• Chickoo trees = $3x = \bf 30$

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Answer 2

Answer:

Appropriate Question :-

• The ratio of numbers of mango trees to chickoo trees in an orchard is 2 : 3. If 5 more trees of each type of are planted the ratio of trees would be 5 : 7. Find the number of mango and chickoo trees in the orchard.

Given :-

• The ratio of number of trees to chickoo trees in an orchard is 2 : 3.
• If 5 more trees of each type of are planted the ratio of trees would be 5 : 7.

To Find :-

• What are the number of mango and chickoo trees in the orchard.

Solution :-

Let,

$\mapsto \bf Number_{(Mango\: Trees)} =\: 2x$

$\mapsto \bf Number_{(Chickoo\: Trees)} =\: 3x$

Now,

$\clubsuit$ If 5 more trees of each type of are planted the seed of trees would be 5 : 7.

So,

$\leadsto \sf Number_{(Mango\: Trees)} =\: (2x + 5)$

$\leadsto \sf Number_{(Mango\: Trees)} =\: (3x + 5)$

According to the question :

$\bigstar$ If 5 more trees of each type of are planted the ratio of trees would be 5 : 7.

So,

$\implies \sf\bold{\pink{\bigg\{\dfrac{Number_{(Mango\: Trees)}}{Number_{(Chickoo\: Trees)}}\bigg\} =\: \bigg\{\dfrac{5}{7}\bigg\} }}$

$\implies \sf \dfrac{(2x + 5)}{(3x + 5)} =\: \dfrac{5}{7}$

By doing cross multiplication we get,

$\implies \sf 5(3x + 5) =\: 7(2x + 5)$

$\implies \sf 15x + 25 =\: 14x + 35$

$\implies \sf 15x - 14x =\: 35 - 25$

$\implies \sf\bold{\purple{x =\: 10}}$

Hence, the required numbers of mango and chickoo trees in the orchard :

$\dag$ Number Of Mango Trees :

$\dashrightarrow \sf Number_{(Mango\: Trees)} =\: 2x$

$\dashrightarrow \sf Number_{(Mango\: Trees)} =\: 2 \times 10$

$\dashrightarrow \sf\bold{\red{Number_{(Mango\: Trees)} =\: 20}}$

$\dag$ Number Of Chickoo Trees :

$\dashrightarrow \sf Number_{(Chickoo\: Trees)} =\: 3x$

$\dashrightarrow \sf Number_{(Chickoo\: Trees)} =\: 3 \times 10$

$\dashrightarrow \sf\bold{\red{Number_{(Chickoo\: Trees)} =\: 30}}$

$\therefore$ The number of mango and chickoo trees in the orchard is 20 and 30 respectively.

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