# The temperature at 12 noon was 10 degree Celsius above zero. If it is decrease at a rate of 2 degree Celsius until midnight at what time will the temperature be 8 degree Celsius below zero. What will be the temperature at midnight?

$\begin{array}{l}\text{Given,}\\ T_1=10^{\circ}\ C\ at\ 12:00\ pm\\ \text{Temprature decrease }2\ ^{\circ}\ C\ per\ hr\\ \text{It is AP series}\ -\ 10,\ 8,\ 6,\ 4,\ .........\\ \text{When temprature will be }-8^{\circ}\ C.\\ T_n=a+\left(n-1\right)d\\ -8=10+\left(n-1\right)\left(-2\right)\\ \Rightarrow n=10\ \\ time\ =10+12\ -1=21\\ \text{So,}\ -8^{\circ}\ C\ at\ 21:00\ pm\\ \text{At midnight,}\ \\ 12:00\ am\ ,\ \text{after 3:00 hr}\\ T=-8^{\circ}\ C\ +\left(-2^{\circ}\ C\times3\right)\\ T=-14^{\circ}\ C\end{array}$

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