Mathematics is the sense you never knew you had | 0–9 with Creativity

A Pathway to solve guesstimate

We are often asked a guesstimate that seems to be a high degree of creativity & it has an actual answer to it already. In that case, we have to prioritize our KPI's very sincerely to minimize the error percentage to the problem statement.

This is my third story at the medium channel, where I am trying to provide a mathematical approach for Estimating the Area of New Delhi.

Let’s talk about some of the assumptions regarding the Problem statement:

• Clarify your understanding of the problem statement and check if you are attempting to solve the right business problem because if this doesn’t start well, the error percentage keeps on increasing with every step
• Clarify every question that comes to your mind and leave no ambiguity; Prioritize the KPI’s well
• Broadly most of the cities/countries are particular in shape. For instance: Delhi tend to be circular in shape as it has a ring road
• While Proceeding with the problem, ask questions to gather more data which will lead you to catch on to important metrics quickly

We can take a minute and think of our own Strategy to approach this.

Delhi has a ring road, so that would suggest that the overall structure of Delhi is circular. So to Figure out if we have landmark physical infrastructure in the city with which we can benchmark our approach. One thing that strikingly comes out is Delhi Metro.

So, we’ll see if Delhi metro can help us solve this case better.
We will take anyone line of Delhi metro line; I am more comfortable with the yellow line. Look at the Delhi metro map & with the yellow line; look at the two extremities with the yellow line. We have Samaypur Badli at one end and
Hooda city center at another.

Delhi Metro Map

What we can see is, it is an approximately straight line, and while solving guesstimate, we’re just looking at an approximate figure, so it doesn’t really matter. The next So next question is if we have to estimate the length of the line??

Before we go towards that, we must share our overall strategy so that the person who is our interviewer doesn’t feel lost, so in this case; our overall strategy would be to identified Delhi as circular in shape.

we can use the area formula for a circle which is,

Area of a Circle, A = πr2 square units, where r = d/2

Now for that to get calculated, we need to figure out what the radius of the city would be?
Assuming the straight line at the entire diameter of the city & from that, we will get the radius. So, the objective here is to find the diameter of Delhi city ??

To do so, I am using the yellow line, as it runs from Amaypur Badli to Hooda city center. Hooda city center lies in Gurgaon, so we can actually discount few stations here.

We actually need something that involves speed and time — a mode of transport through. So I will go ahead with Metro. So, as someone who has already traveled on Delhi metro can take a guess, it takes an hour to travel from Jahangir puri to last station of Delhi might be Chhatarpur and the average speed of metro considering, it takes a lot of stops so maximum speed of metro in Delhi would be like the maximum speed of a car in Delhi, 70–80km/hr because it has to make frequent acceleration, deceleration & stops so I would assume the average speed is roughly around 40–50 km/hr.

Calculation :

As we know, Distance = speed x time
Speed is 40 km/hr & Time is 1 hr.

Assumption: Distance is Diameter as Delhi is circular in shape.
Distance= 40 km hence, r=20 km(d/2)

Let's calculate the Area of Delhi,
Area of a Circle, A = πr2

So, the area comes around 1257 km²
We’ll try to verify the answer with the actual number; it is 1484 km². So we seem to be quite accurate.

The guesstimated area of Delhi is 1257 km²
The actual area of India is 1484 km²

And this 15% error is completely acceptable. It is the approach that matters the most. Try to give a detailed opening point for the problem statement.

We can try a similar approach for other cities. For example, we can try Mumbai. Mumbai has an elongated shape. We can find the length of any of the local train tracks, which is parallel to the city, to get the sense of the length of the city. We can use these measures approximately to find an area of any city/India/globally. All we have to do is to figure out the physical infrastructure of the city.

Let me know your feedback/suggestions on this if we can improvise this any better.

Thanks & Clap :)