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Question
in winter, the temperatures at a hill station from Monday to Friday are in A.P. The sum of the temperatures of Monday, Tuesday and Wednesday is 0° C and the sum of the temperatures of Thursday and Friday is 15° C. Find the temperature of each of the five days.
Solution
Let the temperatures of hill station from Monday to Friday which form are A.P. be a – 2d, a – d, a, a + d, a + 2d respectively.
As per the first condition,
a – 2d + a – d + a = 0
∴ 3a – 3d = 0
∴ 3 (a – d) = 0
∴ a – d = 0
∴ a = d
As per the second condition,
a + d + a + 2d = 15
∴ 2a + 3d = 15
∴ 2a + 3a = 15 [∵ a = d]
∴ 5a = 15
∴ a =`15/5`
∴ a = 3
∴ d = 3 [∵ d = a]
∴ a – 2d = 3 – 2 (3) = 3 – 6 = – 3
∴ a – d = 3 – 3 = 0
∴ a + d = 3 + 3 = 6
∴ a + 2d = 3 + 2 (3) = 3 + 6 = 9
∴ The temperatures from Monday to Friday are – 30C, 00C, 30C, 60C and 90C respectively
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