# How many black cabs are there in London?

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 there are 2.6 million cars in London (Link below). So, we are close. Bravo!!

http://content.tfl.gov.uk/technical-note-12-how-many-cars-are-there-in-london.pdf

The number of black cabs

Now we know that total cars which are cabs must be a small % of total cars. Assuming 5% of total cars are cabs. From first-hand experience you may estimate more that 5% but remember private cars are not always out and about versus a cab which is. So, we get total number of cabs in London as 143k. We have plenty of Ubers and private taxis on the road – no points for getting that right in the interview. So, if 15% of all cabs are black cabs, we get 21,500 black cabs in London.

10 - How do you get exactly 4 litres of water given a 3 litre and a 5 litre bucket. There is no way of measuring partial fills in a bucket?

Let’s start with filling up the five-litre bucket first and pouring the contents into the 3-litre bucket. We now have 2 litres of water remaining in the five-litre bucket.

We empty the three -litre bucket and pour the 2 litres from the bigger bucket in the threelitre bucket.

Fill up the five-litre bucket again and pour water from this bucket into the three-litre bucket up to its brim. Given that the three-litre bucket already had 2 litres of water in it only 1 litre of water is transferred into the three litre-bucket, leaving us with four litres of water in the five-litre bucket.

We can also start with filling up the three-litre bucket first – pour three litres into five litre bucket.

Repeat process and you are left with one litre of water in the three-litre bucket.

Empty five litre bucket and pour one litre from three litre bucket into the five-litre bucket.

Fill up the three-litre bucket up to its brim again and pour into five-litre bucket giving us four litres of water in the five-litre bucket.

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