The ideal way to approach this question is through the supply side. That is, if we are able to estimate the number of pizza restaurants and the number of pizzas each sell a day, we should be able to figure out the number of pizzas sold. Yes there are also pizzas sold at supermarkets which we will keep aside for this one.
First, in trying to estimate the number of pizzas restaurants in London let us first break London into different zones and locations. If you have stayed in London, then you will know that Londoners are proud of their extensive public transport network. Probably the best in the world.
The city has 11 tube lines in addition to a well spread overground rail network. Estimating that each tube line has say around 25 stations we get approximately 275 stations. The real number is 270 stations so we are not far. If in an interview you are 20 to 30% away from the exact number you may be veered back by the interviewer or may be allowed to carry on.
Additonally, lets say London has approximately half as many overground stations as that of the underground. That is approximately 130 overground stations (112 in actuality). All in we get approximately 400 stations in London. You can use the station sizing exercise for a number of other analytical questions such as number of houses sold in London everyday and so on.
Pizza places per station. Assuming that each station has approximately 5 pizza places we get 2,000 pizza places in London.
Pizzas sold per place a day From there on assuming each restaurant takes about 5 minutes per pizza we get 12 pizzas an hour and on a 12 hour work day we get c. 144 pizzas sold per restaurant.
and finally... Multiplying 144 pizzas by c. 2,000 pizza restaurants in London we get 288,000 pizzas sold in the city everyday. Of the approximately 8.5m people living in London everyday that works out to c. 3.5% of the population chomping away at a pizza - Believable? Yes sir! Waiter - A grand margarita for me as well please!! :)
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