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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 sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Solution
The readings of the temperature were in A.P.
Let, first term = a
common difference = d
Temperature of Monday = a
Temperature of Tuesday = a + d
Temperature of Wednesday = a + 2d
Temperature of Thursday = a + 3d
Temperature of Friday = a + 4d
Temperature of Saturday = a + 5d
The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday.
\[\therefore a + \left( a + 5d \right) = 5 + \left( a + d + a + 5d \right)\]
\[ \Rightarrow 2a + 5d = 5 + 2a + 6d\]
\[ \Rightarrow 6d - 5d = - 5\]
\[ \Rightarrow d = - 5\]
Also, the temperature of Wednesday was –30° celsius.
\[\therefore a + 2d = - 30\]
\[ \Rightarrow a + 2\left( - 5 \right) = - 30\]
\[ \Rightarrow a - 10 = - 30\]
\[ \Rightarrow a = - 30 + 10\]
\[ \Rightarrow a = - 20\]
Hence, the temperature on the other five days were:
Monday = –20° celsius
Tuesday = –25° celsius
Thursday = –35° celsius
Friday = –40° celsius
Saturday = –45° celsius
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