Question

In an experiment, a solution of hydrochloric acid is to be kept between $30^{\circ}$ and $35^{\circ}$ Celsius. What is the range of temperature in degree Fahrenheit if conversion formula is given by $C = \frac{5}{9} \left(F - 32\right)$, where $C$ and $F$ represent temperature in degree Celsius and degree Fahrenheit, respectively?

• A. $86\,{}^{\circ}F$ to $96 \,{}^{\circ}F$
• B. $86\,{}^{\circ}F$ to $95 \,{}^{\circ}F$
• C. $36\,{}^{\circ}F$ to $42 \,{}^{\circ}F$
• D. $85\,{}^{\circ}F$ to $95 \,{}^{\circ}F$

Answer 1

Answer: (B)

It is given that $30 < C < 35$.
Putting $C = \frac{5}{9}\left(F - 32\right)$, we get $30 < \frac{5}{9} \left(F - 32\right) < 35$
or $\quad \frac{9}{5} \left(30\right) < \left(F - 32\right) < \frac{9}{5} \times \left(35\right)$
or $\quad 54 < \left(F - 32\right) < 63$ or $86 < F < 95$.
Thus, the required range of temperature is between $86^{\circ}\, F$ and $95^{\circ}\, F$.