Delhi Metro Guesstimate Case Study

Problem statement:

“How many people travel in Delhi metro every day?”

Lets solve this Guestimate question.

Solution:-

Assumptions:

1. Timing of the train rides are from 6 am in morning to 11pm in night.
2. There are two trains moving in opposite directions every 30 min starting from the first ride at 6 am and the last ride at 11 pm.(while standing on a platform of a station one can see 1 train comes to his/ her platform and leaves and other train comes on opposite platform and leaves in opposite direction)
3. Metro train rides are only available for 10 routes and average 20 trains are operational on a particular route for to and fro rides.
4. Once the passenger boards the train for a ride from the starting station, he/she only leaves the train at the end station on the route for a particular ride.
5. There is no ride repetition for passengers.
6. First ride starts at 6 am from the starting station, goes all the way to the end point and reaches the end station at 6: 25 am. At 6:30 the ending station becomes the starting point of the ride and then the train goes all the way to the starting station in the opposite direction and ends the ride.(for example rute = blue line. The train starts its ride 1 from vaishali station and goes all the way to end the ride at dwarka station and then again starts ride 2 from dwarka station to end the ride at vaishali station)
7. A particular train completes 2 rides in 1 hour on one route.
8. Each train has average 6 coaches with the seating capacity of 50 people per coach (all the seats are occupied in every ride.) and there are 100 people on an average traveling standing per coach per ride..

Step 1:

Objective: find the no. of people who travel in Delhi metro every day.

Step 2:

No. of people travels per day =

(passengers traveling in the train per ride)

*

(no. of rides taken by the train in one hour)

*

(how many hours train is operational per day)

*

(no. of routes for which the train is operational)

*

(no. of trains operational on 1 route)

Step 3:

• Passengers traveling in the train per ride =

:- (no. of seated people per coach + average standing passengers per coach)

* (no. of coach per train)

:- (50 + 100) * 6 => 150 * 6 => 900

Step 4 : As per our assumptions and few calculations,

• Passengers traveling in the train per ride = 900
• No. of rides taken by a train in one hour = 2 rides (1 complete ride in to and fro motion)
• How many hours the train is operational per day = 17 hours (6 am to 11 pm)
• No. of routes for which the train is operational = 10
• No. of trains operational on 1 route is = 20

Step 5: Final result as per step 2 = :-

• No. of people travels per day =

900 * 2 * 17 * 10 * 20 => 360000 * 17 => 61,20,000.

Hence on an average 6.12 million people travel in Delhi metro every single day.

Step 6: Sanity Check of the estimated result:

Total population of Delhi = ~ 32 million people.

Hence, 6.12 million people traveling by Delhi metro seems reasonable.