Students in a class planted 100 trees. They planted some fruit trees and some non-fruit trees. The number of non-fruit trees was one more than twice the number of fruit trees. How many fruit trees and non-fruit trees did they plant?

33

and

68

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34

and

67

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33

and

67

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35

and

68

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Solution

The correct option is C $33$ and $67$
Let ' $x$ ' be the number of fruit trees.

According to the question, the number of non-fruit trees would be $1 + 2 x$ .
Total number of trees = 100
$\Rightarrow$ Number of fruit trees + Number of non-fruit trees $= 100$
$x + (1 + 2 x) = 100$
The above algebraic equation represents the scenario given in the question.

Solving this equation to get the value of ' $x$ ',
$x + (1 + 2 x) = 100$
$\Rightarrow 3 x + 1 = 100$

On subtracting '1' from both sides of the equation, we get,
$3 x + 1 - 1 = 100 - 1$
$\Rightarrow 3 x = 99$

On dividing by '3', we get,
$\frac{3 x}{3} = \frac{99}{3}$
$\Rightarrow x = 33$

The number of fruit trees would be $33$ .

Number of non-fruit trees $= 1 + 2 x$
$= 1 + 2 \times 33 = 1 + 66$
$= 67$

The number of non-fruit trees would be $67$ .

$V e r i f i c a t i o n : - -------------- -$
Total number of trees = Number of fruit trees + Number of non-fruit trees
$= 33 + 67$
$= 100$
This is the total number of trees given in the question.

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