Question

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.\[\dfrac{2}{7}\]
B. \[\dfrac{3}{7}\]
C. \[\dfrac{4}{7}\]
D. \[\dfrac{5}{7}\]

Answer 1

Hint: We assume the capacity of bucket as a variable. Then we write the value of capacities of 1 large bottle and 1 small bottle using the variable. Use the given statement and write the equation of fluid left in a large bottle.
* Fraction simply depicts or represents a part of the whole. Fraction is formed when we write a number divided by another number where dividend comes in numerator and divisor comes in denominator. It is of the form \[\dfrac{a}{b}\] which can be written as ‘a’ divided by ‘b’.

Complete step-by-step answer:
Let us assume the capacity of the bucket as ‘x’ litres.
We have two types of bottles small and large.
Since we are given that the fluid contained in a bucket can fill four large bottles, which means that 4 large bottles fills the bucket
\[\because \]Capacity of 4 large bottles \[ = x\]litres
\[ \Rightarrow \]Capacity of 1 large bottle \[ = \dfrac{x}{4}\]litres … (1)
Since we are given that the fluid contained in a bucket can fill seven small bottles, which means that 7 small bottles fills the bucket
\[\because \]Capacity of 7 small bottles \[ = x\]litres
\[ \Rightarrow \]Capacity of 1 small bottle \[ = \dfrac{x}{7}\]litres … (2)
Now we are given that a full large bottle is used to fill an empty small bottle.
We have to calculate the fraction of fluid left over in the large bottle when the small one is full, so we subtract the capacity of one small bottle from the capacity of one large bottle.
\[ \Rightarrow \]Fluid left in the bottle \[ = \dfrac{x}{4} - \dfrac{x}{7}\]
Take LCM in right side
\[ \Rightarrow \]Fluid left in the bottle \[ = \dfrac{{7x - 4x}}{{28}}\]
\[ \Rightarrow \]Fluid left in the bottle \[ = \dfrac{{3x}}{{28}}\] … (3)
Fraction of fluid left in a large bottle is given by dividing the fluid left in a large bottle by the capacity of one large bottle.
\[ \Rightarrow \]Fraction of fluid is \[ = \dfrac{{\dfrac{{3x}}{{28}}}}{{\dfrac{x}{4}}}\]
Write fraction in simple form
\[ \Rightarrow \]Fraction of fluid is \[ = \dfrac{{3x}}{{28}} \times \dfrac{4}{x}\]
Cancel same factors from numerator and denominator
\[ \Rightarrow \]Fraction of fluid is \[ = \dfrac{3}{7}\]
\[\therefore \]Fraction of fluid left in large bottle is \[\dfrac{3}{7}\]

\[\therefore \]Correct option is B.

Note:
Many students make the mistake of writing the fraction obtained in the equation (3) as they think that it is a fraction since it has a numerator and denominator, but we have to calculate the fraction of fluid left in the large bottle which means we have to calculate how much part is filled in large bottle.