Some time after midnight, the temperature was 24 degrees Celsius

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From the question is given that,

Temperature at the beginning i.e., at 12 noon = 10°C

Rate of change of temperature = - 2°C per hour

Then,

Temperature at 1 PM = 10 + (-2) = 10 – 2 = 8°C

Temperature at 2 PM = 8 + (-2) = 8 – 2 = 6°C

Temperature at 3 PM = 6 + (-2) = 6 – 2 = 4°C

Temperature at 4 PM = 4 + (-2) = 4 – 2 = 2°C

Temperature at 5 PM = 2 + (-2) = 2 – 2 = 0°C

Temperature at 6 PM = 0 + (-2) = 0 – 2 = -2°C

Temperature at 7 PM = -2 + (-2) = -2 -2 = -4°C

Temperature at 8 PM = -4 + (-2) = -4 – 2 = -6°C

Temperature at 9 PM = -6 + (-2) = -6 – 2 = -8°C

∴At 9 PM the temperature will be 8°C below zero

Then,

The temperature at mid-night i.e., at 12 AM

Change in temperature in 12 hours = -2°C × 12 = - 24°C

So, at midnight temperature will be = 10 + (-24)

= - 14°C

So, at midnight temperature will be 14°C below 0.