Question

The temperature at 10 a. m. was 12 C above zero. If it decrease at the rate of 3 c per hour until the midnight, at what time would the temperature be 15C below zero? What would be the temperature at midnight.?

Answer 1

Temperature at midnight will be (12-42)°C=-40°C.
and

The time when the temperature will be -15°C is 7 p.m. since total temperature reduced is equal to 27°C and it means that total time taken =27/3 hours=9 hrs and 10+9=19 hrs means 7 P.M.

Answer 2

↑ Here is your answer ↓
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These numbers are in A.P,

$12, 9, 6, ... -15$

Where,

$a = 12 \\ \\ d = -3 \\ \\ a_n = -15$

So,

$a_n = a + (n-1)d$

$-15 = 12 + (n-1)(-3)$

$-15 = 12 -3n + 3$

$-15 = 15 - 3n$

Open now,

$-15 - 15 + 3n = 0$

$-30 + 3n = 0$

$3n - 30 = 0$

$3n = 30$

$n= 30/3$

$n = 10$

Hence, 10 hours after '10 AM',

=> 8 PM

Now,

Temperature at midnight (12'o clock),

=> 4 hours after 8 PM

Temperature drop will be,

$= 4*-3^o C$

$= -12^o C$

So,

$= - 15 + -12$

$= -27^o C$