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A Celsius thermometer and a Fahrenheit thermometer are put in a hot bath. The reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer. The temperature of the hot bath is
A) ${26.67^ \circ }\,C$
B) ${36.67^ \circ }\,C$
C) ${46.67^ \circ }\,C$
D) ${56.67^ \circ }\,C$

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Last updated date: 23rd May 2024
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Answer
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Hint:- The above given problem can be solved using the formula that is derived for the relationship between the Celsius thermometer and the Fahrenheit thermometer of the hot bath where the Fahrenheit thermometer is just 3 times the reading on Celsius thermometer.

Useful formula:
The formula for the relationship between Celsius and Fahrenheit;
$\dfrac{{F - 32}}{{180}} = \dfrac{C}{{100}}$
Where, $F$ denotes the value of Fahrenheit in the Fahrenheit scale, $C$ denotes the value of Celsius in the Celsius scale.

Complete step by step solution:
The data given in the problem is;
Reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer, that is;
$F = 3C$
Therefore, the relationship between Celsius and Fahrenheit;
$\dfrac{{F - 32}}{{180}} = \dfrac{C}{{100}}$
$
  \dfrac{{3C - 32}}{{100}} = \dfrac{C}{{100}} \\
  C = \dfrac{{80}}{3} \\
 $
On simplifying we get;
$C = {26.67^ \circ }\,C$.

Therefore, the temperature of the hot bath according to the Celsius thermometer is $C = {26.67^ \circ }\,C$.

Hence the option (A), $C = {26.67^ \circ }\,C$ is the correct answer.

Note: Since in the problem it is only asked to find the temperature of the water bath Celsius thermometer that in Celsius, we didn’t calculate the temperature of the water bath in Fahrenheit thermometer.