A farmer uses $\frac{2}{5}$ of his land to grow cassava, $\frac{1}{3}$ of the remaining for yam and the rest for maize. Find the part of the land used for maize

$\frac{2}{15}$

$\frac{2}{5}$

$\frac{2}{3}$

$\frac{4}{5}$

Correct answer is B

Let x represent the entire farmland

then, $\frac{2}{5}$ x + $\frac{1}{3}$ [x - $\frac{2}{3}x$ ] + M = x

Where M represents the part of the farmland used for growing maize, continuing

$\frac{2}{5}$ x + $\frac{1}{3}$ x [1 - $\frac{2}{3}x$ ] + M = x

$\frac{2}{5}x + \frac{1}{3}$ x [ $\frac{3}{5}$ ] + M = x

$\frac{2}{5}$ x + $\frac{1x}{5}$ + M = x

$\frac{3x}{5} + M = x$

M = x - $\frac{2}{5}$ x

= x[1 - $\frac{3}{5}$ ]

= x[ $\frac{2}{5}$ ] = $\frac{2x}{5}$

Hence the part of the land used for growing maize is

$\frac{2}{5}$

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