Question

A drum of kerosene is $\dfrac{3}{4}$ full. When 80 liters of kerosene is drawn from it, it remains $\dfrac{1}{2}$ full. Find the capacity of the drum.

Answer 1

Hint: We will find the initial volume of kerosene in the drum. Then we will subtract 80 liters from it. We will get an equation that has an expression on the left-hand side indicating the subtraction of 80 liters from the initial volume of kerosene and on the right-hand side, it will have the volume of kerosene left in the drum in terms of the capacity of the drum. Using this equation, we will find the capacity of the drum.

Complete step-by-step solution
Let the capacity of the drum be $x$ liters. Now, the initial condition states that the drum of kerosene is $\dfrac{3}{4}$ full. So, the initial volume of kerosene in the drum is $\dfrac{3}{4}x$ liters. Now, we are given that 80 liters of kerosene are drawn from the drum and the drum remains $\dfrac{1}{2}$ full. So, the volume of kerosene inside the drum after 80 liters is drawn from it is $\dfrac{1}{2}x$. The 80 liters are drawn from $\dfrac{3}{4}x$ liters, which is the initial volume of kerosene inside the drum. So, we get the following equation,
$\dfrac{3}{4}x-80=\dfrac{1}{2}x$
The above equation is a linear equation in the variable $x$. Multiplying the above equation by 4, we get
$3x-320=2x$
Solving for $x$, we get
 $\begin{align}
  & 3x-2x=320 \\
 & \therefore x=320 \\
\end{align}$
Hence, the capacity of the drum is 320 liters.

Note: The important part of this question is to come up with the correct equation that encompasses the given information and allows us to find the unknown value. The relation between the initial and final volume of kerosene inside the drum should be expressed in the equation that we form. The equation involves fractions so we should be careful while doing the calculations so that we can avoid making any minor mistakes.