Question

If the values of the temperature of a body in Fahrenheit and Celsius scales are in the ratio of 13 : 5, then the temperature of the body is

• A. \(80^\circ \text{F}\)
• B. \(104^\circ \text{C}\)
• C. \(40^\circ \text{C}\)
• D. \(40^\circ \text{F}\)

Hint:

Always remember the relation between Fahrenheit and Celsius: \( F = \frac{9}{5}C + 32 \). Use it carefully when dealing with ratios.

Answer 1

The Correct Option is C

Step 1: Use the conversion formula between Fahrenheit and Celsius: \[ F = \frac{9}{5}C + 32 \] Step 2: Given the ratio \( \frac{F}{C} = \frac{13}{5} \), substitute into the equation: \[ \frac{\frac{9}{5}C + 32}{C} = \frac{13}{5} \Rightarrow \frac{9C + 160}{5C} = \frac{13}{5} \] Step 3: Cross-multiply and solve: \[ (9C + 160) \cdot 5 = 13 \cdot 5C \Rightarrow 45C + 800 = 65C \Rightarrow 20C = 800 \Rightarrow C = 40^\circ \text{C} \]