Question

If the two temperatures on Fahrenheit scale differ by \(54^{\circ}\text{F}\), then the difference in temperature on the Celsius scale is

• A. \(30^{\circ}\text{C}\)
• B. \(35^{\circ}\text{C}\)
• C. \(40^{\circ}\text{C}\)
• D. \(45^{\circ}\text{C}\)

Hint:

The size of one Celsius degree is 9/5 of a Fahrenheit degree.

Answer 1

The Correct Option is A

Step 1: Scale Relation:
\(\dfrac{C}{100}=\dfrac{F-32}{180}\). For a difference, the constant 32 cancels: \(\dfrac{\Delta C}{100}=\dfrac{\Delta F}{180}\).

Step 2: Substitute:
\(\Delta C=\dfrac{100}{180}\times54=\dfrac59\times54=30\).

Step 3: Check the Options:
35, 40 and 45 would need \(\Delta F=63,\ 72,\ 81\). The given difference is 54, so only 30 fits.

Final Answer:
The difference is \(30^{\circ}\)C, option (A). \[ \boxed{\text{(A) } 30^{\circ}\text{C}} \]