Question

# A tin of oil was $4/5$ full. When $6$ bottles of oil were taken out and $4$ bottles of oil were poured into it , it was $3/4$ full. How many bottles of the oil the tin contains initially?A $16$ B $40$ C $32$ D None of these

Hint:
Here we need to apply the concept Proper Fractions and algebra with equation solving. Proper Fraction : A fraction in which the numerator is less than the denominator. We need to find how many bottles of the oil the tin contains initially.

Complete step by step solution:
Let the capacity of the tin be $x$ bottles .
Amount of oil present in the tin is $4/5\times x$
According to the question,
$6$ bottles of oil was taken out,
$\Rightarrow -6$
$4$ bottles of oil were poured into,
$\Rightarrow +4$
After the above changes amount of oil in the tin is $3/4\times x$
\begin{align} & \Rightarrow {}^{4}/{}_{5}\times x-6+4={}^{3}/{}_{4}\times x \\ & \Rightarrow {}^{4}/{}_{5}\times x-2={}^{3}/{}_{4}\times x \\ & \Rightarrow {}^{4}/{}_{5}\times x-{}^{3}/{}_{4}\times x=2 \\ & \Rightarrow {}^{\left( 16x-15x \right)}/{}_{20}=2 \\ & \Rightarrow 16x-15x=2\times 20 \\ & \Rightarrow x=40 \\ \end{align}
Therefore, the capacity of the tin is $40$ bottles.
Hence, Option choice B is the correct answer.

Note:
In such types of questions the concept of Fractions and algebra with equation solving is needed. Here the variables are assigned to unknown values and equations are framed accordingly as per the relation in the question. Then it is solved to get the required value.