Question

The average temperature of the town in the first four days of the month was 58 degrees. The average for the second, third, fourth and the fifth day was 60 degrees. If the temperature of the first and the fifth day were in the ratio \[7:8\]. Then what is the temperature on the fifth day
A.64 degrees
B.62 degrees
C.56 degrees
D.None of these

Answer 1

Hint: First we will find the sum of the temperatures on the first four days by their average. Then we will find the sum of the temperatures on second, third, fourth and the fifth day using their average. Then we will take the sum of the two equations formed leaving us with a relation between the temperatures of the first and the fifth day. As we already have been given another relation between the first and the fifth day we can substitute that in the equation and get the exact temperatures on the first and the fifth day.

Complete step-by-step answer:
Let the temperatures of the five days be represented by \[a,b,c,d,e\] in order. Now as we know the average temperature of the first four days is 58, so their sum of their temperatures will be \[58 \times 4 = 232\]
Thus, it can be written as \[a + b + c + d = 232\] and denoted as equation (1).
Now, the average of the temperatures on second, third, fourth and the fifth day is 60. So the sum of their temperatures will be \[60 \times 4 = 240\]. It can be represented as \[b + c + d + e = 240\] and denote this equation as equation (2).
Now, when we subtract the equation (1) from equation (2), we get \[
  (b + c + d + e) - (a + b + c + d) = 240 - 232 \\
\Rightarrow e - a = 8 \\
\]
This equation \[e - a = 8\] will be denoted as equation (3).
Now, it is already given in the question that the ratio of temperatures of the first and the fifth day were in the ratio \[7:8\]. Thus, we get a relation as \[\dfrac{a}{e} = \dfrac{7}{8}\]. Thus, \[a = \dfrac{{7e}}{8}\]. We will substitute this value of \[a\] in equation (3) to get
\[
   \Rightarrow e - a = 8 \\
   \Rightarrow e - \dfrac{{7e}}{8} = 8 \\
   \Rightarrow \dfrac{{8e - 7e}}{8} = 8 \\
   \Rightarrow \dfrac{e}{8} = 8 \\
   \Rightarrow e = 64 \\
\]
Hence, the temperature on the fifth day was 64 degrees.
Hence, option (A) is the correct option.


Note: The best way of solving such a question is making equations from the conditions given in the question and by adding or subtracting 2 equations such that the variables not required are eliminated from the equation. Here, a simple clue was the ratio of temperatures on the first and fifth day, which clearly indicated that we had to eliminate the rest of the variables and get an equation between temperatures of the first and the fifth day.