# 5. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

H Harsh Kankaria

Given,

Temperature at 12 noon = $10^{\circ}C$

Final temperature = $-8^{\circ}C$

$\therefore$ Decrease in temperature = $10 - (-8) = 18^{\circ}C$

Time taken for the temperature  to decrease by $2^{\circ}C$$1\ hour$

$\therefore$ Time taken for the temperature  to decrease by $18^{\circ}C$

$=\frac{1}{2}\times18\ hour$

$= 9\ hours$

Now,

Time until mignight = $12\ hours$

$\therefore$ Decrease in temperature in $12\ hours$ = $2\times12 = 24^{\circ}C$

Therefore, temparature at midnight = $(10 - 24)^{\circ}C = -14^{\circ}C$

Therefore, temperature at mid-night will be $14^{\circ}C$ below zero.

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