Explanation

(d) The coefficient of performance of a refrigerator is given by $\alpha = \frac{Q_{2}}{W} = \frac{Q_{2}}{Q_{1} - Q_{2}}$
Where, $Q_{1} =$ Amount of heat released to the hot reservoir
$Q_{2} =$ Amount of heat extracts from the cold reservoir
$W =$ work done on the working substance
$\therefore\alpha = \frac{Q_{2}}{Q_{1} - Q_{2}}$
Substituting the given values, we get $\frac{1}{3} = \frac{Q_{2}}{200 - Q_{2}}$
$200 - Q_{2} = 3Q_{2} \Rightarrow 4Q_{2} = 200 \Rightarrow Q_{2} = \frac{200}{4}J = 50J$
$\therefore W = Q_{1} - Q_{2} = 200J - 50J = 150J$