(a) Cloudy days the rate of photosynthesis will decrease because sunlight is necessary for photosynthesis. On a cloudy day, there will be less sunlight.
(b) No rainfall in the area the rate of photosynthesis will decrease because water is one of the raw material needed by plant for photosynthesis. If there is no rainfall in an area, there will be less water available to plant.
(c) Good manuring in the area the rate will increase because plants need raw minerals such as $N$, $P$, $Fe$, $Mg$ etc., for building their body and take these minerals from the soil. Good manuring in the area will increase the amount of these minerals in the soil thus, increasing photosynthesis.