A 14.4 kg 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 is the closest to the percentage difference in the usage of gas per hour, of the smaller burner over the larger burner?
(a)23.07\%
(b)26.23\%
(c)30\%
(d)32.23\%
Answer
Answer (as printed): A
Explanation
Consumption of gas in the smaller burner in 1 hour $$=\left(\frac{14.4}{104}\right) \mathrm{kg}=\frac{9}{65} \mathrm{kg} .$$ Consumption of gas in the larger burner in 1 hour $$=\left(\frac{14.4}{80}\right) \mathrm{kg}=\frac{9}{50} \mathrm{kg} . \text { Difference in consumption }=\left(\frac{9}{50}-\frac{9}{65}\right) \mathrm{kg}=\frac{27}{650} \mathrm{kg} \text {. }$$ Required percentage difference $$=\left(\frac{27}{650} \times \frac{50}{9} \times 100\right) \%=\left(\frac{300}{13}\right) \%=23.07 \% .$$