Question

Two thermometers, one Celsius and other Fahrenheit are put in a hot bath. The reading in the Fahrenheit thermometers is just three times the reading on the Celsius thermometer. The temperature of the bath is
(A) $70$
(B) $80$
(C) $100$
(D) $\left( {\dfrac{{80}}{3}} \right)$

Answer 1

The thermometers are used to measure the temperature of anybody. In this question, Use the formula of the relation between the temperature in the Fahrenheit and the Celsius scale. Substitute the relation between them given in the question in the formula, to know the value of the temperature of the hot bath.

Useful formula:
The relation between the Fahrenheit and the Celsius is
$F = \left( {\dfrac{9}{5}C} \right) + 32$
Where $F$ is the temperature reading in the Fahrenheit and $C$ is the reading in the Celsius of the thermometer.

Complete step by step solution:
It is given that the
Reading of the Fahrenheit thermometer is thrice the reading of the Celsius thermometer.
$F = 3C$
Solving the above equation in the Fahrenheit and the Celsius conversion formula.
$3C = \left( {\dfrac{9}{5}C} \right) + 32$
$3C = \dfrac{{9C}}{5} + 32$
By simplifying the above equation,
$3C = \dfrac{{9C + 160}}{5}$
By cross multiplying the terms on both sides.
$15C = 9C + 160$
By grouping the similar terms in the same side for the easier calculation.
$15C - 9C = 160$
By performing the simple arithmetic operation.
$6C = 160$
$C = \dfrac{{160}}{6}$
By performing the division in the above step.
$C = \dfrac{{80}}{3}$
Hence the temperature of the hot bath in the Celsius thermometer is $\dfrac{{80}}{3}$.

Thus, the option (D) is correct.

Note: In most thermometers, mercury is used to indicate the temperature in it. Remember the formula correctly. Don’t interchange the Celsius and the Fahrenheit temperature terms in the formula, this might result in the wrong answer.