Question

A farmer uses $\frac{11}{18}$ of his field for growing rice and $\frac{3}{7}$ of the remaining field for growing tomatoes. Of the area thus left, he uses $\frac{1}{4}$ of it to grow spinach and rest to grow carrots. What fraction of the field is used for growing carrots ?

• A. $\frac{1}{18}$
• B. $\frac{1}{4}$
• C. $\frac{2}{7}$
• D. $\frac{1}{6}$

Answer 1

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

It is given that a farmer uses $\frac{11}{18}$ of his field for growing rice, which means that $\frac{7}{18}$ of his field is left because $1-\frac{11}{18}=\frac{7}{18}$.

Now, he uses $\frac{3}{7}$ of the remaining field for growing tomatoes that is:

$\frac{3}{7}\times \frac{7}{18}=\frac{3}{18}$

Then, the area left is $\frac{7}{18}-\frac{3}{18}=\frac{4}{18}$

Now, he uses $\frac{1}{4}$ of the left field for growing spinach that is:

$\frac{1}{4}\times \frac{4}{18}=\frac{1}{18}$

Then, the area left is $\frac{4}{18}-\frac{1}{18}=\frac{3}{18}$ which can be rewritten as $\frac{1}{6}$.

Hence, $\frac{1}{6}$ of the field is used for growing carrots.