Guesstimate?—?Cost of painting the pillars of the metro lines in Delhi
Let’s start the guesstimates with a fairly simple question with the focus being on the clarity of the approach and presenting the same in a coherent manner.
This time-based guesstimate was solved by Sahil Grover and myself for a qualifying round of a case study competition in Jan 2015. He’s one amazing teammate!
You may want to read my semi-guide on How to Approach Guesstimates before going ahead with this one.
Q. Guess + Estimate the cost of painting the pillars of the metro lines in Delhi as of today. Also, every pillar consists of an advertisement sized 4X4 feet on each side of the pillar. Thus, every team is required to find the estimated net expenditure. (Cost of painting pillar?—?Revenue received from the advertiser).
Solution-
This question is pretty straightforward. All you’re required to do is estimate the number of pillars, assume values for the cost of painting and revenue earned per pillar. Please note that there are many more parameters that could’ve been considered. We’ll limit it to the below assumptions for simplicity’s sake.
The crucial step here is to estimate the number of pillars. We try to visualize how any metro line looks like. It starts from a station and ends at another. There are turns, splits and intermediary stations. The line itself may be underground, on-ground or above the ground. Let’s assign the number of pillars for each of these situations, taking care to choose simple numbers (multiples of 2, 5 or 10):
- Since the underground/ground level stations will not have any pillars, we will assume the number of pillars for them to be zero. The connections to the preceding and subsequent stations, however, will be taken into account.
- The station itself, will have more number of pillars, owing to the extra strength required for the stability of the station premises, therefore, we will assume 8 pillars for each station above ground level.
- The number of pillars increases for every turn/split(like the one after Yamuna Bank) in the tracks. We will assume the increase on the basis of the length of the track.
- For every 100m, there is a pillar. Therefore, there are 10 pillars in each km.
Basis the above assumptions, the length of the various Metro Lines, and subsequently, distance between two stations is assumed to be as follows:
Though the data above has been taken from the official website, it is not necessary to do so. You may assume whole numbers by general knowledge. For instance, you may already know that the blue line is the longest followed by yellow. Assign say, 50 and 45 to each respectively.
Now, once the number of pillars are calculated, we can estimate the cost of painting the pillars as well as the revenue. The following figures have been taken arbitrarily //not a recommended approach:
- Assume the cost of painting each pillar to be Rs 1200.
- Assume the revenue from each advertisement placed to be 2500.
The total expenditure, therefore, is Rs. (21,85,000).
In this example, we may have used the following parameters as well:
- Assigning a higher revenue to popular areas (Cost of advertising would be higher) and lesser revenue for those less popular.
- The above step would lead to the segregation of the metro line’s distance into densely populated/less populated areas. Alternatively, we may also choose to list the most well known stations where the advertising cost is bound to be higher.
- Inculcate the metro lines still in construction and their pillars.
- We could have also assumed specific dimensions for the diameter and the height of the pillars, subsequently arriving at its area and multiplying the same with the cost of painting per square unit area.
What more do you think we could’ve considered? What could’ve been better? More to come!