Question
Answers

A tin of oil was $ \dfrac{4}{5} $ full. When 6 bottles of oil was taken out and 4 bottles of oil was poured into it was $ \dfrac{3}{4} $ full. How many bottles of oil can the tin contain?
(a) 10
(b) 20
(c) 30
(d) 40

Answer Verified Verified
Hint: First, a process is done in which 6 bottles of oil is taken out and then 4 bottles of oil is poured into it to get the tin as $ \dfrac{3}{4} $ full and we are given with the condition that $ \dfrac{4}{5} $ of the tin is full. Then, from the above two conditions, we get that $ \dfrac{3}{4} $ of x is subtracted from $ \dfrac{4}{5} $ of x then the number of bottles of oil changes from 6 to 4. Then, solve the above expression to get the value of x which is the number of bottles required to fill the tin.

Complete step-by-step answer:
In this question, we are supposed to find the number of bottles required to fill the tin completely.
So, before proceeding for this, we need to suppose the number of bottles be x.
Then, we are given the condition that $ \dfrac{4}{5} $ of the tin is full.
Then, a process is done in which 6 bottles of oil are taken out and then 4 bottles of oil is poured into it to get the tin as $ \dfrac{3}{4} $ full.
Now, from the above two conditions, we get that $ \dfrac{3}{4} $ of x is subtracted from $ \dfrac{4}{5} $ of x then the number of bottles of oil changes from 6 to 4.
So, we get the expression for the following condition as:
 $ \dfrac{4}{5}x-\dfrac{3}{4}x=6-4 $
Then, solve the above expression to get the value of x which is the number of bottles required to fill the tin as:
 $ \begin{align}
  & \dfrac{16x-15x}{20}=2 \\
 & \Rightarrow \dfrac{x}{20}=2 \\
 & \Rightarrow x=40 \\
\end{align} $
So, the required number of bottles to fill the tin completely is 40 bottles.
So, the correct answer is “Option D”.

Note: Now, to solve these types of questions we must be careful with the calculations of the questions as this is only a mistake we can make as the question is very simple and straightforward. Moreover, we must be aware of the fact that $ \dfrac{4}{5} $ is greater than $ \dfrac{3}{4} $ to get the answer correctly.