Questions & Answers

Question

Answers

(a) 10

(b) 20

(c) 30

(d) 40

Answer
Verified

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.