A body cools from 50^ ^ ^ C to 45^ ^ ^ C in 5 minutes, and...

Using Newton's law of cooling in approximate form:

\dfrac{T_1 - T_2}{t} = K \left(\dfrac{T_1 + T_2}{2} -T_0 \right)

For the first interval:

\dfrac{50 - 45}{5} =$K \left( \dfrac{50 + 45}{2} - T_0 \right)$

$1 = K (47.5 - T_0)$

For the second interval:

\dfrac{45 - 40}{8} = K \left(\dfrac{45 + 40}{2} -T_0 \right)

\dfrac{5}{8} =$K (42.5 - T_0)$

Dividing the two equations:

\dfrac{8}{5} = \dfrac{47.5 - T_0}{42.5 - T_0}

$8(42.5 - T_0) = 5(47.5 - T_0)$

$340 - 8T_0 = 237.5 - 5T_0$

$3T_0 = 102.5$

$T_0 = 34.16^\circ C \approx 34^\circ C$