Question

Temperature of a body can be measured on different scales,Celcius (C) and Fahrenheit (F).When thermometers measuring ${}^{0}C$ and ${}^{0}F$ were used to measure temperatures of various bodies,the following table was obtained

	${}^{0}C$	${}^{0}F$
Ice	0	32
Boiling water	100	212
Hot water	70	158
Tap water	25	$F_1$

Then $F_1$ is

• A. 77
• B. 57
• C. 88
• D. 91

Answer 1

The correct option is A 77

Let the temperature on Fahrenheit scale can be written as $F=AT+B$

where $T$ is the temperature in Celcius.

Ice ; $T=0^{o}C$, we have $F={32}^{o}F$

$\therefore$ $32=A\times 0+B$

$⟹$ $B=32$

Boiling water : $T={100}^{o}C$, we have $F={212}^{o}F$

$\therefore$ $212=A\times 100+32$

$⟹$ $A=\frac{9}{5}$

Hence in Fahrenheit scale, $F=\frac{9}{5}T+32$

Now, for tap water : $T={25}^{o}C$

$F_1=\frac{9}{5}\times 25+32={77}^{o}F$