Question

A bottle is $80\% $full. The liquid in the bottle consists of $60\% $ guava juice and $40\% $ pineapple juice. The remainder of the bottle is then filled with $200$ mL of rum. How much guava juice is in the bottle?
A.$350mL$
B.$480mL$
C.$500mL$
D.$460mL$

Answer 1

Hint: Here, we will be using the concept of percentage, percentage means per 100, which is a number expressed as a fraction of 100 such as:
\[
  40\% {\text{ }}of{\text{ }}200 = \dfrac{{40}}{{100}} \times 200 \\
   = 40 \times 2 \\
   = 80 \\
 \]
It means 40% of 200 is 80.
In the question, we first need to determine the total capacity of the bottle and then, the percentage of each juice after filling the empty part of the bottle with rum.


Complete step by step solution:
A bottle is $80\% $full of guava and pineapple juice.
First, we have to assume the unknown value because all the given terms are co-related and we don’t have the exact value of the juice.
Let b be the total capacity of the bottle.

The bottle has a total capacity of $1000$ml.
Now we can use the successive percentages to figure out the total amount of guava juice.
Guava juice is $60\% $of $80\% $ of the juice initially in other words guava juice is $60\% $ of $80\% $ of $1000$. Hence,

Guava juice is $480$ ml of total juice.
Option B is the correct option.


Note: In these types of problem where the successive percentage is given, we can calculate fractions such as \[\dfrac{2}{3} \times \dfrac{4}{5} = \dfrac{8}{{15}}\]. Alternatively, we can solve this problem as: $\dfrac{{60}}{{100}} \times \dfrac{{80}}{{100}} \times 1000 = 480$ directly.