A body cools from `60^(@)C` to `50^(@)C` in 10 minutes . If the room temperature is `25^(@)C` and assuming Newton's law of cooling to hold good, the temperature of the body at the end of the next 10 minutes will be

Options

A. `38.5^@C`
B. `40^@C`
C. `42.85^@C`
D. `45^@C`

Answer

C

Explanation

`(T_1-T_2)/(t)=K((T_1 +T_2)/(2) -T_0)`
`(60 -50)/(10)=K((60+50)/(2)-25)`
and `(50-T)/(10)=K ((50+T)/(2)-25)`
By (i) and (ii) -
`(10)/(50-T)=((60+50)/(2)-25)/((50+T)/(2)-25)`
`implies T=42.85^@C`