Question

The average temperature for the first 5 day of the year is ${40^\circ }C$ and the average temperature from 2nd to 6th day is $42^\circ C$ and the ratio b/w the temperature of 1st day and the 6th day is 3:4, find the temperature of the sixth day.

Answer 1

Hint: Here, at find we will be finding the average temperature of one particular day and on that basis and in accordance with the question, we will find the temperature of the 6th day.

Complete step-by-step answer:
The average temperature of the first five days of the year = ${40^\circ }C$
So, the first five days of the year include the first day, the second day, the third day, the fourth day and the fifth day.
Therefore, total temperature of first day to the fifth day of the year is
     $ = 5 \times {40^\circ }C$
     \[ = {200^\circ }C\]
According to the question.
Average temperature of 2nd day to 6th day $ = {42^\circ }C$
Again, it comprises the second day, third day, fourth day, fifth day and sixth day, which is altogether five days.
Therefore the total temperature of the second day to the sixth day is equal to.
     = 5 days $ \times {42^\circ }C$ ( average temperature )
     = $\underline {{{210}^\circ }C} $
Now, we know that temperature from 1st to 5th day is
${200^\circ }C$ and total temperature from second day ( 2nd ) to 6th day is ${210^\circ }C$
So, to get the difference between the temperature, we have to find the difference between the total temperature from second day to sixth day and the total temperature from first day to fifth day
$\therefore $ Difference b/w temperature
     $ = {210^\circ }C - {200^\circ }C$
     $ = {10^\circ }C$ (1)
Given that, the ratio of b/w the 1st day temperature to 6th day is 3:4.
So let the temperature of the 1st day be $3x$ and that of the 6th day is 4x.
So, let’s consider the temperature of the first day and the 6th day have the same difference in temperature. This can be said from $eq$ ①.
$\therefore 4x - 3x = {10^\circ }C$
$x = {10^\circ }C$
As we get the value of ‘x’ to be ${10^\circ }C$
$\because $ The value of temperature of 1st day = 3x
          $ = 3 \times 10 = {30^\circ }C$
and the value of the temperature on the 6th day is 4x.
          $ = 4 \times 10 = {40^\circ }C$
     Hence, 6th day temperature = ${40^0}C$

Note: In this type of question the difference remains the same throughout the question following that we can solve very early.