A farmer uses \(\frac{2}{5}\) of his land to grow cassava, \(\frac{1}{3}\) of the remaining for...
MATHEMATICS
WAEC 2015
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. \(\frac{2}{5}\)
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
\(\frac{2}{5}\)
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