Question

30 acres of land were to be distributed among 45 farmers equally. Each farmer cultivates 3 different crops in equal areas, in his land. What is the area of cultivation available for one kind of crop for a farmer?

• A. $\frac{2}{9}$
• B. $\frac{1}{3}$
• C. $\frac{5}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is A $\frac{2}{9}$

Since 30 acres are to be divided among 45 farmers equally, each farmer would get $\frac{30}{45}$ acres.


The above rectangle represents the part of land each farmer gets. As each farmer cultivates 3 different crops in equal area, the land would have to be divided into 3 equal regions. Hence, we divide $\frac{30}{45}$ by 3, i.e $\frac{\frac{30}{45}}{3}$ or multiply $\frac{30}{45}$ by the reciprocal of 3, i.e $\frac{30}{45}\times \frac{1}{3}$
The area of cultivation available for one kind of crop for a farmer is:
$\frac{30}{45}\times \frac{1}{3}=\frac{10}{45}=\frac{2}{9}$.
$\therefore$ The area of cultivation available for one kind of crop for a farmer is $\frac{2}{9}$.