Question

A \[{\text{14}}{\text{.4kg}}\] 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 the larger burner?
A. \[26\% \]
B. \[32\% \]
C. \[30\% \]
D. \[25\% \]

Answer 1

Hint: According to the question, we can first try to calculate the consumption every hour by the smaller burner and larger burner. For this we need to divide the total capacity by the total number of hours.

Complete step-by-step solution:
According to the question, the total capacity of the gas cylinder is given as \[{\text{14}}{\text{.4kg}}\].
The number of hours when the smaller burner on the gas stove is fully opened is given as \[104\] hours.
Now, to find the gas consumed by the smaller cylinder in \[1\] hour is done by unitary method:
\[{\text{ = }}\dfrac{{{\text{Total}}\,{\text{capacity}}\,{\text{of}}\,{\text{gas}}}}{{{\text{Total}}\,{\text{time}}\,{\text{for}}\,{\text{the}}\,{\text{smaller}}\,{\text{burner}}}}\]
\[{\text{ = }}\dfrac{{{\text{14}}{\text{.4kg}}}}{{{\text{104hours}}}}\]
\[{\text{ = 0}}{\text{.1384kg}}\,{\text{per}}\,{\text{hour}}\]
Similarly, we will find the gas consumed by the larger cylinder in \[1\] hour is done by unitary method:
\[ = \dfrac{{{\text{Total}}\,{\text{capacity}}\,{\text{of}}\,{\text{gas}}}}{{{\text{Total}}\,{\text{time}}\,{\text{for}}\,{\text{the}}\,{\text{larger}}\,{\text{burner}}}}\]
\[ = \dfrac{{{\text{14}}{\text{.4kg}}}}{{{\text{80hours}}}}\]
\[{\text{ = 0}}{\text{.18kg}}\,{\text{per}}\,{\text{hour}}\]
The number of hours when the larger burner on the gas stove is fully opened is given as \[80\] hours.
Now, we need to find the difference in gas consumed between the smaller burner and the larger burner. The difference is:
\[{\text{ = (0}}{\text{.18 - 0}}{\text{.1384)kg}}\,{\text{per}}\,{\text{hour}}\]
\[{\text{ = 0}}{\text{.0416kg}}\,{\text{per}}\,{\text{hour}}\]
Therefore, the difference is \[{\text{0}}{\text{.0416kg}}\,{\text{per}}\,{\text{hour}}\].
Now, we will calculate the percentage difference of the consumption of gas between both the smaller and larger burner and we will get:
\[ \Rightarrow {\text{Percentage = }}\left[ {\dfrac{{{\text{difference}}}}{{{\text{gas}}\,{\text{consumed}}\,{\text{by}}\,{\text{smaller}}\,{\text{burner}}}}} \right]{{ \times 100}}\]
\[ \Rightarrow {\text{Percentage = }}\left[ {\dfrac{{0.0416}}{{0.1384}}} \right]{{ \times 100}}\]
\[ \Rightarrow {\text{Percentage = 0}}{{.3003 \times 100}}\]
\[{\text{ = 30% }}\,{\text{(approximately)}}\]
Therefore, the percentage difference for the gas consumption between the smaller and larger burner is \[{\text{30% }}\,{\text{(approximately)}}\].

Hence the correct answer is option ‘C’.

Note: The above method is very easy and the question is solved very quickly. But many people get confused and make a mistake. While calculating the percentage, they take the gas consumed by a larger burner in the denominator. While calculating the percentage, we always have to take the smaller or initial value in the denominator.