Question

The temperature at which the fahrenheit and celsius scales will give numerically equalvalue

a) - 40 °F and 40°

b) 11.43 °F and 11.43 °C

C)11.43 °F and -11.43 °C

d) both b and c

Don't copy paste​

Answer 1

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Given :- }}}$

$\textsf{ \to The temperature at Celsius and Farenheit are numerically equal .}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: To \ Find :- }}}$

$\textsf{ \to The numerical value .}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Answer :- }}}$

Given that the temperature at Celsius and Farenheit are numerically equal .Let us take that temperature be x , We know the relation between Farenheit and Celsius as ,

$\sf:\implies\pink{ \dfrac{Celsius}{5}=\dfrac{ Farenheit - 32}{9}}\\\\\sf:\implies \dfrac{x}{5}=\dfrac{x-32}{9}\\\\\sf:\implies 9x = 5(x-32)\\\\\sf:\implies 9x = 5x - 160 \\\\\sf:\implies 9x - 5x = (-160) \\\\\sf:\implies 4x = -160 \\\\\sf:\implies x=\dfrac{-160}{4} \\\\\sf:\implies \underset{\red{\bf Option A}}{\underbrace{\boxed{\qquad\pink{\mathfrak x = -40 \qquad}}}}$

$\underline\textsf{\blue{ \therefore Hence the required temperature is \textbf{ -40 ^{\circ} C or -40 ^{\circ} F }. }}$

Answer 2

Relationship between temperature in Fahrenheit and Celsius:-

F = (9/5)C + 32

If the temperature in (t), then as per condition

t = (9/5)t + 32

⇒ t - 9/5 t = 32

⇒ (5 - 9)/5 t = 32

⇒ - ⅘t = 32

⇒ t = 32 × (- 5/4)

⇒ t = - 40

∴ (a) is the correct answer.