Question

The average temperature of the first three days of a week is \[{27^{\circ}}C\] and the next three days is ${29^{\circ}}C$.
If the weekly average is ${28.5^{\circ}}C$. What is the temperature on the last day?
A. ${31.5^{\circ}}C$
B. ${28^{\circ}}C$
C. ${21^{\circ}}C$
D. ${42^{\circ}}C$

Answer 1

Hint: In order to solve this question we will first apply the formula to take the average of n numbers since there are 7 days in a week so we will consider the temperature of the first 3 days as ${27^{\circ}}C$ as it is given in the question that the average of first three days is ${27^{\circ}}C$ and of next three days is ${29^{\circ}}C$ and finally we will suppose the temperature of last day and put it equal to ${28.5^{\circ}}C$. After appropriate calculations, we will get the final answer.

Complete step by step Solution:
For solving this question we will first apply the formula for calculating the average of n numbers:
Average of n numbers = sum of n numbers/n
Since we know that there are 7 days in a week so for this question the value of n will be 7:
As it is stated in question that the average temperature of the first three days is ${27^{\circ}}C$ so the temperature that for three days will be:
 $27 \times 3$
Now similarly it is given that the average temperature of the next three days is ${29^{\circ}}C$ so the temperature for these three days will be:
$29 \times 3$
From the above data, we got the full information for six days and the last day’s temperature we will let is a variable say x;
Now putting these values in the formula;
$\dfrac{{(27 \times 3) + (29 \times 3) + x}}{7} = 28.5$
Now we will substitute all the terms on the other side and put the x on one side after some calculations;
$x = 28.5 \times 3 - \{ (27 \times 3) + (29 \times 3)\} $
On further solving we get;
$x = {31.5^{\circ}}C$

So the correct option is A.

Note:
While solving this question we should keep in mind that we cannot take the first three days as one unit and the next three days in one unit and the last as the third and divide it by 3 and then make the appropriate calculation because it will give the wrong answer.