A new scale of temperature called TIME is introduced. The reading on the new scale is twice the reading on the new scale is twice the reading on a celsius scale when the temperature of a certain body is 373 K. The reading on a Fahrenheit scale is found to (17/15)th the reading on TIME scale when the temperature of a body is `20^(@)C`. Determine the upper fixed point and lower fixed point of the TIME scale.

Explanation

let `.^(T)` represent the temperature in TIME scale.
373K `=100^(@)C`
`U=200.^(T)`
`(20-0)/(100)=(F-32)/(180)`
`(20)/(100)=(F-32)(180)`
`F-32=18xx2`
`F=36+32=68^(@)F`
Temperature on TIME scale corresponding to `20.^(@)C`
`=(68xx15)/(17)=60.^(@)C`
`(68-32)/(180)=(60-L)/(200-L)`
`(200-L)=300-5L`
`4L=100` ltBrgt `L=25.^(@)T`
`therefore` The lower fixed point and upper fixed point are `25.^(@)T` and `200.^(@)T`, repspectively.