Given that $${{\log \,P} \over {y - z}} = {{\log \,Q} \over {z - x}} = {{\log \,R} \over {x - y}} = 10$$ for $$x \ne y \ne z$$, what is the value of the product PQR?

A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15th July of the same year?

The annual average rainfall in a tropical city is 1000 mm. On a particular rainy day (24-hour period), the cumulative rainfall experienced by the city is shown in the graph. Over the 24-hour period, 50% of the rainfall falling on a rooftop, which had an obstruction-free area of 50 m², was harvested into a tank. What is the total volume of water collected in the tank in liters?

Consider a sequence of numbers $${a_1},{a_2},{a_3},....,{a_n}$$ where $${a_n} = {1 \over n} - {1 \over {n + 2}}$$, for each integer n > 0. What is the sum of the first 50 terms?