In winter the temperature at 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 temperature of Thursday and Friday is 15. Find the temperature of each of the five days.

Answer:
Since the temperature at hill station from Monday to Friday is in A.P.
Let us assume those 5 days temperature be
Monday = a – 2d
Tuesday = a – d
Wednesday = a
Thursday = a + d
Friday = a + 2d

According to first condition
a – 2d + a – d + a = 0
∴ 3a – 3d = 0 ------------- eq. no. (1)

According to second condition
a + d + a + 2d = 15
∴ 2a + 3d = 15 -------------eq. no. (2)

Adding eq. (1) and eq. (2)

3a – 3d = 0
2a + 3d = 15
5a  + 0  = 15

∴ a = 15/5

∴ a = 3

Substituting   a = 3 in eq. (2)

2a + 3d =  15
∴ 2(3) + 3d = 15
∴ 6 + 3d = 15
∴ 3d = 15 – 6
∴ 3d = 9
∴ d = 9/3
∴ d = 3
Monday = a – 2d = 3 – 2(3) = 3 – 6 = - 30 C
Tuesday = a – d  = 3 – 3 = 00 C
Wednesday = a = 3 0 C
Thursday = a + d = 3 + 3 = 60 C
Friday = a + 2d = 3 + 2(3) = 3 + 6 = 90 C

∴ The temperature from Monday to Friday are
- 3 0 C, 00 C, 30 C, 60C and 90C respectively.  

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