Question

A man uses 1/3 of his land for growing mangoes, 1/4 for bananas, 3/8 for apples, and the remaining 18 hectors for oranges


question1) Area of land used to grow mangoes and bananas

Answer 1

        $\text{\huge \bf \underline{Answer:}}$

        $\text{Let the total area of the land be }x$

$\implies \: \text{Area of land used for growing mangoes} = \dfrac13x\: \text{hectors}$

$\implies \: \text{Area of land used for growing bananas} = \dfrac14x\: \text{hectors}$

$\implies \: \text{Area of land used for growing apples} = \dfrac38x \: \text{hectors}$

$\implies \: \text{Area of land used for growing oranges} = 18 \: \text{hectors}$

        $\text{The total area of land} = x$

$\implies \: x = \dfrac13x + \dfrac14x + \dfrac38x + 18$

$\implies \: x - 18 = \dfrac13x + \dfrac14x + \dfrac38x$

$\implies \: x - 18 = \dfrac{8x + 6x + 9x}{24}$

$\implies \: x - 18 = \dfrac{23x}{24}$

$\implies \: 24(x - 18) = 23x$

$\implies \: 24x - 432 = 23x$

$\implies \: 24x - 23x = 432$

$\implies \: x = 432 \text{ hectors}$

$\implies \: \boxed{\boxed{\text{Area of land used to grown mangoes} = \dfrac13 \times 432 = 144 \text{ hectors}}}}$

$\implies \: \boxed{\boxed{\text{Area of land used to grown bananas} = \dfrac14 \times 432 = 108 \text{ hectors}}}}$

$\implies \: \boxed{\boxed{\text{Area of land used to grown apples} = \dfrac38 \times 432 = 162\text{ hectors}}}}$

Answer 2

Answer:

==> (x/3)+(x/4)+(3x/8)+18=x

==> 7x/12)+(3x/8)+18=x

==> (56x)+(36x)+(18*96)=96x

==> 4x=18*96

==> x=18*24

==> x=432

mango = 432/3= 144 hector

banana= 432/4= 108 hector

mango+ banana= 144+108=252hectors