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Answers
QuEsTioN :
Kargil's temperature was recorded in a week from Monday to Saturday . All readings were in A.P. , the sum of temperatures of Monday and Saturday was 5° C more than the sum of temperatures of Tuesday and Saturday . If temperature of Wednesday was -30° C then , find the temperature on other 5 days .
SoluTioN :
Given that the temperatures readings on the days of a week from Monday to Saturday were in A.P.
therefore, Let
Reading on Monday = a₁
Reading on Tuesday = a₂
Reading on Wednesday = a₃
Reading on Thursday = a₄
Reading on Friday = a₅
Reading on Saturday = a₆
where the first term of A.P. is a and common difference is d
Now, According to the first information Given
Sum of the temperatures of Monday and Saturday was 5° C more than the sum of temperatures of Tuesday and Saturday
so,
↦ a₁ + a₆ = 5 + a₂ + a₆
↦ a₁ = 5 + a₂
↦ a = 5 + a + d
↦ d = -5
Hence, the common difference is -5
According to Second information given
Temperature of Wednesday is -30° C
so,
↦ a₃ = -30
↦ a + 2 d = -30
putting d = -5
↦ a + 2 (-5) = -30
↦ a - 10 = -30
↦ a = -20
Hence , the first term of AP is -20
So,
● Temperature on Monday = a₁ = a = -20° C
● Temperature on Tuesday = a₂ = a + d = -20 - 5 = -25° C
● Temperature on Wednesday = a₃ = a + 2 d = - 20 + 2 ( - 5 ) = -30° C
● Temperature on Thursday = a₄ = a + 3 d = -20 + 3 (-5) = -35° C
● Temperature on Friday = a₅ = a + 4 d = -20 + 4 (-5) = -40° C
● Temperature on Saturday = a₆ = a + 5 d = -20 + 5(-5) = -45° C