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.  

Answer 1

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