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Estimate the number of tube lights used in a big city (10 Million Population).

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Here is how I would approach this solution:

1. Asking clarifying questions: Tubelights vary in size. Do I need to consider a specific size for the tube light? Should I include any bulbs or CFLs too? Do I need to consider defected/burned out tube lights? Do we have data related to income levels of the people in the city or can I assume that the city in consideration is Ahmedabad (or any other city preferred by you)?

Now, assuming that we are only considering the tube lights of all sizes (and not any bulbs/CFLs) currently in use for the city of Ahmedabad, we can approach in the following manner:

2. Make an equation: Tubelights will have many uses in a city. Based on that, the equation can be written as:

Number of tube lights = (Number of households * Average number of tube lights per household) + (Number of office complexes * Average number of tube lights per office complex)

Office complexes include everything from hospitals, schools to multinationals etc.

3. Jot down points that you know:

  • The average household size in India is 5
  • People living below the poverty line or without any house represent 15% of the population
4. Review and state your assumptions: I am taking the following assumptions:
  • 15% of the households belong to the lower class and have, on an average, two tube lights per household
  • 50% of the households belong to the middle class and have, on an average, 5 tube lights per household
  • 20% of the households belong to the high class and have, on an average, 8 tube lights per household
  • Small schools, clinics, and police stations use, on an average, 20 tube lights
  • Big ones use, on an average, 40 tube lights
  • Multinational corporations and malls use, on an average, 80 tube lights
  • Number of small schools is around 500, small clinics is also around 100 and small police stations is around 50
  • Corresponding number for big entities is around 50, 10 and 5 respectively
  • Number of multinational corporations is around 10
  • Number of malls is around 5
5. Do the math:
For households: (1,500,000/5 * 2) + (5,000,000/5 * 5) + (2,000,000/5 * 8) = 8,800,000 tube lights
For office complexes: ((500+100+50)*20) + ((50+10+5)*40) + ((10+5)*80) = 16,800 tube lights
So, total number of tube lights used in a big city is 88,16,800.
 
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