Question

A tin of oil was \[\dfrac{4}{5}\] full when size six bottles of oil were taken out and four bottles of oil were poured in it was \[\dfrac{3}{4}\] full. How many bottles of oil did the tin contain initially?

Answer 1

Hint: In the above question we will assume the number of bottles of oil to be x. Also, it is given that six bottles of oil are taken out and four bottles of oil are poured in it which means there are net two bottles of oils are taken out.

Complete step-by-step answer:
Let us assume the number of bottles of oil to be x. Also, we have been given that six bottles of oil are taken out and four bottles of oil are poured in it which means there are net two bottles of oils are taken out.

\[\Rightarrow \dfrac{4}{5}x-\dfrac{3}{4}x=2\]

Now, to solve the above expression first of all find the L.C.M of denominators which we will get 20. So convert both the fractions by changing their numerator and denominator and making them like fractions.

\[\begin{align}

  & \Rightarrow \dfrac{1}{20}x=2 \\

 & \Rightarrow x=40 \\

\end{align}\]

Therefore, the total number of bottles of oil is 40 which the tin contains initially.


Note: The key to solving this question is understanding the question properly and formulating the right equations. So, it is necessary that we read the question two to three times and then start the solution. Just be careful while solving the equation as there is a chance that you might make a mistake while taking LCM & further solving it.