Question

The fluid contained in a bucket can fill four bottles or seven small bottles. A full large bottle is used to fill empty small bottles. What fraction of the fluid is left over in the large bottle when the small one is full?
A. \[\dfrac{2}{7}\]
B. \[\dfrac{3}{7}\]
C. \[\dfrac{4}{7}\]
D. \[\dfrac{5}{7}\]

Answer 1

Hint: The given question give the details for the volume of the larger tank to the smaller when the fluid is poured from larger to smaller tanks or bottles, here we have to use unit conversion method to get the volume of smaller and larger bottles, and then on solving further we can get the exact volume leftover according to the question.

Complete step by step answer:
The give question gives the brief explanation for the ration of smaller and larger volumes of the tanks given in the question, and we have to find the leftover liquid after filling it to the larger bottles from the main tank to the larger bottles, on solving we get:
Let the capacity of tank be “x” liters,
Capacity of one large bottle=\[\dfrac{x}{4}\]
Capacity of one small bottle=\[\dfrac{x}{7}\]
Fluid left in large bottle=\[\dfrac{x}{4} - \dfrac{x}{7} = \dfrac{{3x}}{{28}}\]
Required fraction=\[\dfrac{{\dfrac{{3x}}{{28}}}}{{\dfrac{x}{4}}} = \dfrac{3}{7}\]
Here we have first calculated the volume for larger bottles and then for smaller bottles, by assuming a whole volume of fluid, then we found the left over volume between larger and smaller bottles, finally dividing both the fractions we get the required fraction asked in the question.

Note: The given question is for simplifying the details by doing the conversion of whole volume to a fixed volume of bottle, and this needs to be solved by the conversion of volume to single bottles, as we calculated in the above question.