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 the larger burner?
(a) 26.23 %
(b) 30 %
(c) 32.23 %
(d) 23.07 %

Answer 1

Hint:First of all, find the value of the consumption per hour by smaller and larger burners by dividing total capacity by total hours. Now use the below formula to find the required answer.
\[\left[ \dfrac{\left( \text{Consumption by larger stove} \right)-\left( \text{Consumption by smaller stove} \right)}{\left( \text{Consumption by smaller stove} \right)} \right]\times 100\]

Complete step-by-step answer:
Here, we are given that 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. We have to find the approximate value of the percentage difference in the usage of gas per hour, between the smaller and the larger burner.
We are given that the total capacity of the gas cylinder = 14.4 kg.
Also, we are given that when the smaller burner is opened, the total time for which the gas cylinder runs = 104 hours.
So, we get the gas consumed by smaller cylinder per hour \[=\dfrac{\text{Total capacity of the gas cylinder}}{\text{Total time for the smaller burner}}\]
\[=\dfrac{14.4kg}{104\text{ hours}}\]
Hence, we get the consumption of gas by smaller burner per hour = 0.1334 kg/hr…….(i)
Now, we are given that when the larger burner is opened, the total time to which the gas cylinder runs = 80 hours.
So, we get the gas consumed by the larger burner per hour \[=\dfrac{\text{Total capacity of the gas cylinder}}{\text{Total time for the larger burner}}\]
\[=\dfrac{14.4kg}{80\text{ hours}}\]
Hence, we get the consumption of the gas by larger burner per hour = 0.18 kg/hour……(ii)
Now, we have to find the percentage difference in the usage of gas per hour. First of all, let us find the actual difference in the usage of gas per hour, we get,
The difference in the usage of gas (D) = (Consumption of gas by larger burner per hour) – (Consumption of gas by smaller burner per hour)
By substituting the respective value of RHS from equation (i) and (ii), we get,
\[D=0.18kg/hr-0.1384kg/hr\]
\[D=0.0416kg/hr.....\left( iii \right)\]
So, we get the percentage difference between usage of the gas per hour and consumption of gas by smaller and larger burner,
\[P=\left( \dfrac{D}{\text{Consumption of gas by smaller burner}} \right)\times 100\]
By substituting the values of RHS from equation (iii) and (ii), we get,
\[P=\left( \dfrac{0.0416}{0.1384} \right)\times 100\]
\[=\left( 0.3003 \right)\times 100\]
\[\approx 30\]%
Hence, option (b) is the right answer.

Note: In this question, some students make this mistake of taking the consumption by a larger burner that is 0.18 kg/hr in the denominator while calculating the percentage which is wrong. While calculating the percentage change or the percentage difference between any two values, we always have to use the formula
\[\left[ \dfrac{\left( \text{Final Value} \right)-\left( \text{Initial Value} \right)}{\left( \text{Final Value} \right)} \right]\times 100\]