Q107 / 150 · MHT CET 2026 (19 April Shift 1) · Physics
If the two temperatures on Fahrenheit scale differ by $54^\circ\text{F}$, then the difference in temperature on the Celsius scale is
- Correct answerA$30^\circ\text{C}$
- B$35^\circ\text{C}$
- C$40^\circ\text{C}$
- D$45^\circ\text{C}$
Solution
The relation between the Fahrenheit and Celsius temperature scales is given by:
$F = \dfrac{9}{5}C + 32$
Taking the difference for two temperatures, we get:
$\Delta F = \dfrac{9}{5}\Delta C$
Given that the difference on the Fahrenheit scale is $\Delta F = 54^{\circ}\text{F}$, substituting this value yields:
$54 = \dfrac{9}{5}\Delta C$
$\Delta C = 54 \times \dfrac{5}{9}$
$\Delta C = 30^{\circ}\text{C}$
The difference in temperature on the Celsius scale is $30^{\circ}\text{C}$.
Answer: $30^\circ\text{C}$
$F = \dfrac{9}{5}C + 32$
Taking the difference for two temperatures, we get:
$\Delta F = \dfrac{9}{5}\Delta C$
Given that the difference on the Fahrenheit scale is $\Delta F = 54^{\circ}\text{F}$, substituting this value yields:
$54 = \dfrac{9}{5}\Delta C$
$\Delta C = 54 \times \dfrac{5}{9}$
$\Delta C = 30^{\circ}\text{C}$
The difference in temperature on the Celsius scale is $30^{\circ}\text{C}$.
Answer: $30^\circ\text{C}$
Hence, the correct answer is option: 'A'.