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# A farmer uses $$\frac{2}{5}$$ of his land to grow cassava, $$\frac{1}{3}$$ of th...

### Question

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

### Options

A) $$\frac{2}{15}$$

B) $$\frac{2}{5}$$ C) $$\frac{2}{3}$$

D) $$\frac{4}{5}$$

### Explanation:

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

$$\frac{2}{5}$$