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
A. \(\frac{2}{15}\) B. \(\frac{2}{5}\) C. \(\frac{2}{3}\) D. \(\frac{4}{5}\)
Correct Answer: B
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 \(\frac{2}{5}\)