Question

A drum of kerosene oil is \[\dfrac{3}{4}\] full. When 30 liters of oil are drawn from it, it is \[\dfrac{7}{12}\] full. Find the capacity of the drum.
A. 120 liters
B. 140 liters
C. 180 liters
D. 240 liters

Answer 1

Hint: To solve such types of questions we assume the capacity of the vessel as some variable let us say as x and then we use the given conditions in the question to make an equation and solve it to get the value of the variable x.

Complete Step-by-Step solution:
Given that the drum of oil which is \[\dfrac{3}{4}\]full, when 30 liters of oil are drawn from it , it is \[\dfrac{7}{12}\]full. We have to find the capacity of the drum.
Let the total capacity of vessel be \[x\],
Therefore, according to the given condition, the kerosene in the drum is \[\dfrac{3}{4}x\] .
Also given that if 30 liters of kerosene is taken out then the volume of the kerosene in the drums turns out to be \[\dfrac{7}{12}x\],
While writing the above in terms of equation we get the required equation as,
\[\dfrac{3}{4}x-30=\dfrac{7}{12}x\]
Rearranging the equation,
\[\Rightarrow \]\[\dfrac{3}{4}x-\dfrac{7}{12}x=30\]
\[\begin{align}
  & \Rightarrow \dfrac{3(2)x-4(1)x}{12}=30 \\
 & \Rightarrow \dfrac{(6-4)x}{12}=30 \\
 & \Rightarrow \dfrac{2x}{12}=30 \\
 & \Rightarrow 2x=30(12) \\
 & \Rightarrow x=\dfrac{360}{2} \\
 & \Rightarrow x=180 \\
\end{align}\]

Therefore, we get the value as \[x\] = 180 liters, which becomes the volume of the given vessel.
Hence, the capacity of the given vessel is 180 liters, which is option (c).

Note: The possibility or error in the question is starting the question by assuming the wrong given condition and making the wrong equation, which definitely gives an incorrect solution. Hence, always first analyze and then make equations to get the result.