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A hot body is placed in cooler surroundings. When the body temperature is 75°C, the rate of cooling is 4°C/ min. When it is 55°C, the rate of cooling is 2°C/ min. The temperature of the surroundings is

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25°C

35°C

20°C

30°C

answer is D.

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Detailed Solution

$\large \frac {-d\theta}{dt}\propto (\theta -\theta_0);\;4\propto (75-\theta_0);\;2\propto (55-\theta_0)$
$\large \frac 42=\frac {75-\theta_0}{55-\theta_0};\;\theta_0=35^0C$

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