Question

$\text{A single bottle of apple juice contains}1\frac{1}{4}\text{L}\text{of juice. If so, what is the}minimum\text{number}\text{of bottles that have to be opened to fill a 6 L}\text{jar completely?}$

• A. 4
• B. 5
• C. 6
• D. 3

Answer 1

The correct option is B 5

$\text{Amount of juice in a bottle}=1\frac{1}{4}L=\frac{(4\times 1)+1}{4}L=\frac{5}{4}L$

$\text{Amount of juice in 3 bottles}=3\times \frac{5}{4}L=(\frac{5}{4}+\frac{5}{4}+\frac{5}{4})L=\frac{(5+5+5)}{4}L=\frac{15}{4}L=3\frac{3}{4}L<6L$

$\text{Amount of juice in 4 bottles}=4\times \frac{5}{4}L=(\frac{5}{4}+\frac{5}{4}+\frac{5}{4}+\frac{5}{4})L=\frac{(5+5+5+5)}{4}L=\frac{20}{4}L=5L<6L$

$\text{Amount of juice in 5 bottles}=5\times \frac{5}{4}L=(\frac{5}{4}+\frac{5}{4}+\frac{5}{4}+\frac{5}{4}+\frac{5}{4})L=\frac{(5+5+5+5+5)}{4}L=\frac{25}{4}L=6\frac{1}{4}L>6L$

$\text{So, the amount of juice in 4 bottles is}less\text{than 6 L and the amount of juice in}\text{5 bottles is slightly}more\text{than 6 L.}$

$\therefore \text{In order to fill a 6 L jar completely, a}minimum\text{of 5 bottles of juice have to be}\text{opened.}$