Question

In winter, the temperatures at a hill station from Monday to Friday are in A.P. The sum of the temperatures from Monday to Wednesday is $0$, while the sum of the temperatures on Thursday and Friday is $15$. Find the temperatures on each of the weekdays.

Answer 1

Step 1: Assuming variables

Let the temperatures of the hill station from Monday to Friday be $a–2d,a–d,a,a+d,a+2d$ respectively. Here $d$ represents the common difference between the AP.

Step 2: Writing equations from the given conditions

As we know the sum of the temperatures from Monday to Wednesday is $0$ so,

$$\begin{gathered} \Rightarrow a–2d+a–d+a=0 \\ \Rightarrow 3a-3d=0 \\ \Rightarrow a-d=0 \\ \Rightarrow a=d\dots .\left(i\right) \end{gathered}$$

As we know the sum of the temperatures from Thursday and Friday is $15$ so,

$$\begin{gathered} \Rightarrow a+d+a+2d=15 \\ \Rightarrow 2a+3d=15\dots \dots \left(ii\right) \end{gathered}$$

Step 3: Solving (i) and (ii)

$2a+3d=15$ [ from (i) we know that $a=d$]

$$\begin{gathered} \Rightarrow 2a+3a=15 \\ \Rightarrow 5a=15 \\ \Rightarrow a=3 \end{gathered}$$

So $a=d=3.$

Hence temperatures on Monday, Tuesday, Wednesday, Thursday, and Friday are $-3º,0º,3º,6º,9º$ respectively.