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

Can you make it simple please

Solution:

From the problem we get that:

The temperature at 12 noon is 10^{o} C.

The rate of fall of temp. is 2^{o}C per hour.

The total fall of temp. = 10^{o}C to 0^{o}C from 0^{o}C to -8^{o}C = 18^{o}C

Since the temp. to fall 2^{o} it takes 1 hour

The temp. to fall 18^{o} the time taken will be 1/2 x 18 = 9 hours.

Since the present time is 12 noon and if it takes 9 hours to reach the temp. of -8^{o}C.

Then the time at which the temp. will be -8^{o}C = 9 pm in the night.

Since the temp. at 9 pm is -8^{o}C, the temp at 12 midnight will be (12 - 9 = 3 Hours).

Since falls @ 2^{o} per hour, in 3 hour it will fall = 3 x 2 = 6^{o}.

Then the temp. at midnight will be -8^{o}C + (-6^{o}C) = -14^{o}C.

**Ans: 9 pm in the night -14 ^{o}C.**

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