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: Option 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})