The temperature at 12 noon was 10^oC above zero. If it decreases at the rate of 2^oC per hour

until mid-night, at what time would the temperature be 8^oC below zero? What would be the temperature at mid-night?

It is given in the question that,

Temperature at 12 noon = 10^oC

Also,

Change in temperature per hour = - 2^oC

Therefore,

Temperature at 1:00 PM = 10^oC + (-2^oC) = 8^oC

Temperature at 2:00 PM = 8^oC + (-2^oC) = 6^oC

Temperature at 3:00 PM = 6^oC + (-2^oC) = 4^oC

Temperature at 4:00 PM = 4^oC + (-2^oC) = 2^oC

Temperature at 5:00 PM = 2^oC + (-2^oC) = 0^oC

Temperature at 6:00 PM = 0^oC + (-2^oC) = - 2^oC

Temperature at 7:00 PM = - 2^oC + (-2^oC) = - 4^oC

Temperature at 8:00 PM = - 4^oC + (-2^oC) = - 6^oC

Temperature at 9:00 PM = - 6^oC + (-2^oC) = - 8^oC

Hence,

The temperature will be 8^oC below zero at 9:00 PM

Now,

Change in temperature in 12 hours = - 2^oC × 12

= - 24^oC

Also,

At midnight the temperature will be = 10 + (-24)

= - 14^oC

Hence,

The temperature at midnight will be 14^oC below zero