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 temeratures of Tuesday and Saturday. If temperature of Wednesday was `-30@`C Then find the temperature on the other five days.

Answer

The temperature at Kargil for the week were `-20@C,-25@C,-30@C,-35@C,-40@C,-45@C` respectively.

Explanation

The temperature are in A.P. …(Given) Let the temperatures, in `@C`, from Monday to Saturday be `a-3d`, `a-2d`, `a` ,`a+d` and `a+2d` respectively.
The temperature on Wednesday is `-30@C.` i.e.
`a-d=-30` …(Given) …(1)
The sum of the temperatures on Monday and Saturday = the sum of the temperatures on Tuesday and Saturday `+5@C`
`therefore(a-3d)+(a-2d)=(a-2d)+(a+2d)+5`
`thereforea-3d=a-2d+5`
`therefore2d-3d=5`
`therefore-d=5`
`therefored=-5" "...(2)`
Substituting `d=-5` in equation (1),
`a-(-5)=-30`
`thereforea+5=-30`
`thereforea=-30-5` `thereforea=-35" "...(3)`
Substituting the values of and d from (3) and (2),
`a-3d=-35-3(-5)=-35+15=-20`,
`a-2d=-35-2(-5)=-35+10=-25`,
`a-d=-30`, ...[From(1)]
`a=-35`, ...[From(3)]
`a+d=-35(-5)=-35-5=-40,`
`a+2d=-35+2(-5)=-35-10=-45`.