Let's Paint a Metro in Guesstimates

Finally, we reach a point in our module where we can start solving guesstimates. We will look at solving an interesting guesstimate. Are you ready?

Let's begin.

Wasn’t that brilliant!!?

Let us walk through the entire process once more to get a clearer understanding of how Soumya solved the guesstimate.

Problem Statement - What is the cost of paint required to paint a metro?

To begin with, we will first start by understanding and clarifying a few assumptions in order to make the problem-specific. But before we do that, let us understand something else. What type of guesstimate is this?

Since we are to find the cost of paint, we need to find the area of the metro to be painted. Hence, this is most definitely a Geometry or Shape-Based Guesstimate.

Now, we move on to clarifying a few assumptions to narrow down the scope of the problem at hand.

Clarifications

• Do we have to paint one metro or do we have to paint more?
• What part of the metro do we want to paint? Is it the outside including the roof, the inside along with the seats and poles and the roof?
• Would Delhi metro as a reference be acceptable? And in that case, is it a four, six or an eight coach metro?
• How many coats of paint are required to be done?
• And most importantly, what is the cost of the paint?

Based on our clarifications, we might get the following assumptions to take forward from the interviewer.

Assumptions

• We have to paint only one metro.
• We have to paint the outside of the metro, including the roof, we can exclude the interiors.
• The Delhi metro is taken as reference and we can go with a six coach metro (using a proxy).
• The paint is very high quality so one coat is enough.
• The cost of the paint can be assumed to be Rs 1000/litre.

Let us now move to solve. To calculate the cost of paint, we need to calculate the amount of paint. To do that, we must know the area of the surface to be painted for which we need to guesstimate the dimensions of a metro compartment.

Calculating the length

• Approximate size of one seat (focus on the breadth of seat), enough for one person and then some more - 40 cm * 40 cm
• Scale it up to the size of benches - either 8 seats or 2 seats in a bench. Their distribution is three 8-seater and two 2-seater benches (40*8)*3 = 960 and (40*2)*2 = 160
• 4 doors in one coach - area occupied by door equal to the area occupied by one 2-seater bench (40*2)*4= 320
• An extra area at the end of the coaches (50*4) = 200 cm
• Total length = 960 + 160 + 320 +200 = 1540 cm ~ 15 m

Calculating the breadth

• 4 people can stand side by side comfortably (2 on each side of the pole), approximately  (40*4) = 160 cm
• Add two rows of seats (50X2) = 100 cm (to account for the backrest)
• Total breadth = 160 + 100 = 260 cm ~2.5 m

Calculating height

• 50 from the bottom + 50 of the seat = 100 cm
• 1 A3 poster (60 cm length) + empty space to fit two seats = 60 + 50 + 50 = 160
• Total height = 100 + 160 = 260 cm ~ 250 cm ~2.5m
• Another approach - can assume the coach to be cuboidal with breadth and height equal

Area 1 = L*B (roof - 1 per coach) = 15 * 2.5 = 30 + 7.5 = 37.5 ~ 40 square metres

Area 2= L*H (sides - 2 per coach) = 15 * 2.5 = 37.5 ~ 40 square metres

Area 3 = B*H (front and back - 2 per train) = 2.5 * 2.5 = 6.25 ~ 5 square metres

(Increasing and decreasing by similar magnitudes to make calculation easy and also keep the answer accurate)

Number of coaches = 6

Total area = A1 * 6 + A2 * 12 + A3 * 2

 = 40* 6 + 40 * 12 + 5 * 2 = 240 + 480 + 10 = 730 square metres

Now to figure out how much paint is required for painting 1 sq m, you can take proxies. Imagine how much of the wall you can paint with 1l, I’m sure you must have spilt water at one point or the other, how much can a 1l water bottle cover? About 5-6 sq m? Let’s reduce it to 5 for ease of calculation and accounting for the difference viscosity in water and paint.

Hence, 1 Litre can cover 5 square metres. Therefore, 730/5 = 146 Litres of paint will be required to paint the metro.

Considering 5% of wastage, we get a rough figure of about 150 Litres.

Therefore, the total cost will be Rs 150,000.

See how easy that was when approached smartly!

Let us move to yet another example of a guesstimate to further our grip on the topic.