Question

# 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

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.

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.
$\dfrac{4}{5}x-\dfrac{3}{4}x=6-4$
\begin{align} & \dfrac{16x-15x}{20}=2 \\ & \Rightarrow \dfrac{x}{20}=2 \\ & \Rightarrow x=40 \\ \end{align}
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.