There are typically two ways to answer sizing questions such as these – Demand side and Supply side.
When it comes to sizing this question using demand side there are several data points such as # of cars, what % of Londoners use black cabs during the day and multiple demographics inputs which will see us throwing a lot of spaghetti on the wall without a guarantee of any of them sticking. So, the best route to take for this one is supply side.
We first need to estimate the number of cars on road in London (supply of cars) – after which we will take a % of these cars being cabs or black cabs to get to an approximate answer. Let’s start with approximating the number of people with driving license in London.
The number of people with driving license.
Let’s drive off first with estimating the population of London. Knowledgeable candidates will know that London houses around 9m people. Not everyone can drive a car, so let’s break the population down by age groups.
People, who can drive are typically in the 18-72 years bracket. Assuming the average Londoner lives up to the age of 80, we get 66% of total population eligible to drive a car or ~6m people.
Not every Londoner can afford a driving license, so let’s strike out 20% to get 4.8m people who have a driving license in London.
The number of cars in London
Not everyone with a driving License owns a car. Assuming, only 50% of total license holders own a car, we get 2.4m car owners in London.
Now, some of the owners will have more than 1 car. Let’s assume that 15% of owners have 2 cars on an average, we get a total car population of 2.9m cars in London.
We have done some due diligence (Not that you will be able to do this during the interview – if you are lucky the interviewer will second your estimate) and found that