The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?
(a)$\frac{2}{7}$
(b)$\frac{3}{7}$
(c)$\frac{4}{7}$
(d)$\frac{5}{7}$
Answer
Answer (as printed): B
Explanation
Let the capacity of the bucket be $x$ litres. Then, Capacity of 1 large bottle $=\frac{x}{4}$; Capacity of 1 small bottle $=\frac{x}{7}$. Fluid left in large bottle $=\left(\frac{x}{4}-\frac{x}{7}\right)=\frac{3 x}{28}$. $$\therefore \quad \text { Required fraction }=\left(\frac{3 x / 28}{x / 4}\right)=\left(\frac{3 x}{28} \times \frac{4}{x}\right)=\frac{3}{7} .$$
Explanation as extracted from the printed page; notation may be imperfect.