Question

A 1 sq. km circular field is divided into 3 equal plots. If each plot is shared among 2 farmers, the area allotted to each farmer is sq. km

• A. $\frac{1}{6}$
• B. $\frac{3}{2}$
• C. $\frac{2}{3}$
• D. $\frac{1}{12}$

Answer 1

The correct option is A $\frac{1}{6}$


$\text{The shaded region represents}\frac{1}{3}$

$\text{If the area of the whole is given as 1 sq. km}$

$\text{The area of its third}=\frac{1}{3}\text{of}1=\frac{1}{3}\text{sq.km}$

$⟹\text{Area of each plot}=\frac{1}{3}\text{sq. km}$

$\text{Now, each plot is equally shared among}\text{2 farmers.}$

$\text{Area allotted to each farmer}=\frac{1}{3}\text{sq. km}÷2$

$\text{Calculating}\frac{1}{3}÷2\text{using the}keep-change-flip\text{method.}$


$\text{Calculating}\frac{1}{3}\times \frac{1}{2}\text{, we get:}$

$\frac{1}{3}\times \frac{1}{2}=\frac{1\times 1}{3\times 2}=\frac{1}{6}$

$\therefore \text{The area allotted to each farmer is}\frac{1}{6}\text{sq. km.}$