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?

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?

$$\underbrace {{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,.......\,{\rm{ + }}\,{\rm{a}}}_{{\rm{n}}\,{\rm{times}}} = {a^2}b$$ and $$\underbrace {b\,{\rm{ + }}\,b\,{\rm{ + }}\,b\,{\rm{ + }}\,.......\,{\rm{ + }}\,b}_{m\,\,{\rm{times}}} = a{b^2}$$, where a, b, n and m are natural numbers. What is the value of $$\left( {\underbrace {b\,{\rm{ + }}\,b\,{\rm{ + }}\,b\,{\rm{ + }}\,.......\,{\rm{ + }}\,b}_{n\,\,{\rm{times}}}} \right)\left( {\underbrace {a\,{\rm{ + }}\,a\,{\rm{ + }}\,a\,{\rm{ + }}\,.......\,{\rm{ + }}\,a}_{m\,\,{\rm{times}}}} \right)$$?

"His face ___________ with joy when the solution of the puzzle was _______ to him."

The words that best fill the blanks in the above sentence are