Question

A 14.4 kg of gas cylinder runs for 104 hours when the smaller burner on the gas stove is fully opened while it runs for 80 hours when the larger burner on the gas stove is fully opened. Which of these values are the closest to the percentage difference in the usage of gas per hour between the smaller and larger burner?
A. 26%
B. 32%
C. 30%
D. 25%

Answer 1

Hint: Find the gas consumed by a smaller burner and larger burner. Then find their difference in gas consumption per hour. Thus find the percentage difference in usage of gas per hour with respect to the smaller burner.

Complete answer:
We have been given the capacity of the gas cylinder = 14.4 kg.
The smaller burner on the gas stove runs for 104 hours and it runs for 80 hours when the larger burner is on.
Now let us find the gas consumed by smaller burner \[=\dfrac{Capacity\text{ }of\text{ }gas\text{ }cylinder}{Hours\text{ }of\text{ }burning}\]
\[\therefore \]Gas consumed by the smaller burner \[=\dfrac{14.4kg}{104hr}=0.1384{}^{kg}/{}_{hr}\].
Now let us find the gas consumed by the larger burner.
The gas consumed by large number \[=\dfrac{Capacity\text{ }of\text{ }gas\text{ }cylinder}{Hours\text{ }of\text{ }burning}\]
\[\therefore \]Gas consumed by large number \[=\dfrac{14.4kg}{80hr}=0.18{}^{kg}/{}_{hr}\]
Thus we got the gas consumed by both smaller and larger burners.
We were asked to find the percentage difference in the usage of gas per hour between the smaller and the larger burner.
Thus, the difference in consumption per hour = Gas consumed by larger burner – gas consumed by smaller burner
\[\therefore \]Difference in consumption per hour \[=\text{ }\left( 0.18-0.1384 \right){}^{kg}/{}_{hr}=0.0416{}^{kg}/{}_{hr}\].
Thus the percentage difference \[=\dfrac{{}^{Difference\text{ }in\text{ }consumption}/{}_{hour}}{Gas\text{ }consumed\text{ }by\text{ }smaller\text{ }burner}\times 100\]
\[\begin{align}
  & =\dfrac{0.0416}{0.1384}\times 100 \\
 & =\dfrac{416}{1384}\times 100=0.3\times 100=30\% \\
\end{align}\]
Thus we got the percentage difference in the usage of gas per hour between the smaller and larger burner as 30%.

Option C is the correct answer.

Note:
Here the smaller burner works at a lower rate, so less gas per time, than the larger burner. So if we use the larger burner there would be a percentage increase in the gas consumption. Thus we use the smaller one as the gas consumption is less.