Question

4.
In winter, the temperature at a hill station from Monday to Friday is in A. P. The sum of the
temperatures of Monday, Tuesday and Wednesday is zero and the sum of the temperatures of
Thursday and Friday is 15. Find the temperature of each of the five days.

show with complete solution ​

Answer 1

$\underline{ \sf \fcolorbox{red}{pink}{ \huge{Solution :)}}}$

Let , the temperature of each of the five days be

Monday = a – 2d

Tuesday = a – d

Wednesday = a

Thursday = a + d

Friday = a + 2d

Because , the temperature at a hill station from Monday to Friday is in A.P

First Condition : The sum of the temperatures of Monday, Tuesday and Wednesday is zero

a – 2d + a – d + a = 0

3a – 3d = 0 --------- eq (1)

Second Condition : the sum of the temperatures of thursday and friday is 15

a + d + a + 2d = 15

2a + 3d = 15 --------- eq (2)

Adding eq (1) and eq (2) , we get

3a – 3d + 2a + 3d = 0 + 15

5a + 0 = 15

a = 15/5

a = 3

Substituting a = 3 in eq (2) , we get

2a + 3d = 15

2(3) + 3d = 15

6 + 3d = 15

3d = 15 – 6

3d = 9

d = 9/3

d = 3

Therefore , the temperature from Monday to Friday are -3 °C , 0 °C , 3 °C , 6 °C and 9 °C respectively

_____________ Keep Smiling :)

Answer 2

$\huge\mathfrak\green{Heya!!}$

$\huge\mathfrak\red{Answer:-}$

Let us assume that the temperatures of five days be as follows:

Monday: a - 2d

Tuesday: a - d

Wednesday: a

Thursday: a + d

Friday: a + 2d

As given in the question that the temperature at hill station from Monday to Friday is in A.P, so there arise two cases:

Case 1 : The sum of temperatures of Monday , Tuesday and Wednesday is zero(0). That is:

a - 2d + a - d + a = 0

= 3a - 3d = 0 ________(equation 1)

Case 2: The sum of the temperatures of Thursday and Friday is 15. That is:

a + d + a + 2d = 15

= 2a+ 3d = 15________(equation 2)

Comparing equation 1 and 2, we get:

3a - 3d + 2a + 3d = 0 + 15

5a + 0 = 15

a = 15/5

a = 3

Substituting a = 3 in equation 2 we get:

2a + 3d = 15

2(3) + 3d = 15

6 + 3d =15

3d = 15 - 6

3d = 9

d = 9/3

d = 3

Hence, the temperatures from Monday to Friday are:

-3°C

0°C

3°C

$\huge\mathfrak\purple{Hope it helps!!}$