Ex 1.3, 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?Temperature at 12pm = 10°C
Temperature decreases at 2°C per hour
We need to find
Time when temperature is 8°C below zero, i.e., −8°C
∴ Total decrease = Final temperature − Initial Temperature
= −8°C − 10°C
= −8 − 10
= −(8 + 10)
= −18°C
Now,
Total decrease = Temperature decrease in 1 hour × Total number of hours
(𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒)/(𝑇𝑒𝑚𝑝𝑒𝑎𝑡𝑢𝑟𝑒 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 1 ℎ𝑜𝑢𝑟) = Total number of hours
Total number of hours = (𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒)/(𝑇𝑒𝑚𝑝𝑒𝑎𝑡𝑢𝑟𝑒 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 1 ℎ𝑜𝑢𝑟)
Total number of hours = (−𝟏𝟖)/(−𝟐)
Total number of hours = 18/2
Total number of hours = 9
So, in 9 hours, temperature becomes −8°C
∴ Temperature is – 8°C at 9 PM
Also, we need to find temperature at mid-night
Temperature at 12 AM − Temperature at 12 PM
= Temperature change in 12 hours
Now,
Temperature change in 1 hour = −2°C
Temperature change in 12 hours = −2 × 12°C
= −24°C
Now,
Temperature at 12 AM − Temperature at 12 PM
= Temperature change in 12 hours
Temperature at 12 AM − 10°C = −24°C
Temperature at 12 AM = −24 + 10 °C
Temperature at 12 AM = −(24 − 10) °C
Temperature at 12 AM = −14°C
Therefore,
Temperature at mid-night = −14°C

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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