The average temperature of a city for the first sixteen days of January is 22°C, and the average temperature for the last sixteen days of the same month is 26°C. If the average temperature for the entire month is 24°C, what is the temperature on the sixteenth day?  

Correct option is A

Given:

​Average temperature of a city for the first sixteen days of January = 22°C

Average temperature for the last sixteen days of the same month = 26°C

Average temperature for the entire month = 24°C

Formula Used:

Average = $$\frac{\text{Sum of all values}}{\text{Total number of values}}$$​​

Solution:

As per the question,

Average of 15 days temperature + 16th day = 22°C

Sum of the temperatures for first sixteen days = 16 $$\times$$​ 22 = $$352\degree C$$​​

16th day + Average of last 15 days temperature = 26°C

Sum of the temperatures for last sixteen days = 16 $$\times$$​ 26 = $$416\degree C$$ 

Total number of days in the month = 31

Total sum of temperature for the month = 31 $$\times$$​ 24 = 744

So, as per the condition,

Temperature on 16th day + Total sum of temperature of month = Sum of the temperatures for first sixteen days + Sum of the temperatures for last sixteen days

Temperature on 16th day + 744 = 352 + 416

Temperature on 16th day = 768 - 744 = $$\bf 24\degree C$$​​