Below are three problems which are dealing with the concept of averages while measuring temperatures.
The temperature during first day of a week is 37 degree celsius and that of during last day is 32 degree celsius. If the temperature of these two days are excluded, the average temperature of the remaining days is 2 degree celsius lesser than the average temperature of the week. What is the average temperature of the week (in degree celsius)?
a) 29 b) 29.5 c) 30.5 d) 32.5
Answer : b) 29.5
Let the average temperature of the week be X degree.
Then, the total temperature of the whole week is 7X degree....(1)
And the total temperature of the first and last day = 37+32 = 69 degree....(2)
Since the average temperature of the remaining 5 days is 2 degree less than the average degree of the week.
Then the average degree of the remaining 5 days = X-2 degree.
And, the total degree of the remaining 5 days = 5(X-2)...(3)
Therefore, we can comfortably form an equation like the one below :
Total Temperatures of 7 Days = Total Temperature Of First and Last days + Total Temperature of Remaining Five Days.
Or Total Temperatures of 7 Days - Total Temperature Of First and Last days = Total Temperature of Remaining Five Days
Substituting values from our findings above (labelled 1,2 and 3), the above equation becomes,
7X - 69 = 5(X-2)
7x - 5X = 69-10
2X = 59
X = 29.5
Hence, the average temperature of the week is 29.5 degree
There are 4 cups of tea. The average temperature of first 3 cups is 84 degree Celsius and that of last three cups is 80 degree. The temperature of last one is 5/7 th of the first one. Then the temperature of the last one is
a) 30 b) 29 c) 30.5 d) 32
Answer : a) 30
Let the temperature of the 4 cups of tea be T1, T2, T3, T4 respectively.
Now, the average temperature of first 3 cups is 80 degree Celc4us.
i.e., (T1 + T2 + T3)/3 = 84
So, (T1 + T2 + T3) = 84x3 = 252 ...eqn1
From Second condition,
(T2 + T3 + T4)/3 = 80
So, (T2 + T3 + T4) = 80x3 = 240 ...eqn2
And from third condition we can write,
T4 = 5/7x t1 ...eqn3
Substitute T4 = 5/7 x T1 in eqn2
T2 + T3 + 5/7 x T1 = 240 ...eqn4
Now, from eqn1, T2 + T3 = 252 - T1 and Substitute in eqn4,
252 - T1 + 5/7 x T1 = 240
- T1 + 5/7 x T1 = -12
T1 = 42 degree
So T4 = 5/7 x 42 = 30
Then the temperature of last one is 30 degree.
The average temperature of days from Sunday to Tuesday is 35 degree. If the average temperature of Sunday and Monday be 32 degree and that of Monday and Tuesday be 33 degree, then by how much temperature Monday is cooler than Sunday ?
a) 30 degree b) 25 degree c) 15 degree d) 14 degree
Answer : d) 1 4degree
Let S, M, T represents the respective temperature of Sunday, Monday and Tuesday. Then, we have:
From first condition, (S + M + T) / 3 = 35 degree
S + M + T = (35 x 3) = 105 ....eqn1
From the 2nd condition,
S + M = (32 x 2) = 64 ....eqn2
M + T = (33 x 2) = 66 ....eqn3
Adding eqn2 and eqn3, we get: S + 2M + T = 130 .... eqn4
Subtracting eqn1 from eqn4, we get : M = 25
Monday's temperature = 25degree.
From eqn2, S = 64 - M = 64 - 25 = 39
Then Sunday's temperature = 39 degree.
Thus the required difference = 39 - 25 = 14.
Hence the answer is 14 degree.
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