EasyPhysical Estimation

Estimate the number of red cars in Delhi

Scope it first — questions to ask

· Delhi NCT (~20M people) or full NCR with Gurgaon/Noida (~33M)? Scope: NCT Delhi only.
· Cars on the road today, or all-time registrations (which include scrapped vehicles)? Scope: cars actively on the road.
· Private cars only, or taxis/commercial too? Scope: all four-wheeler cars.

Assumptions on the table

· Delhi population ≈ 20M; household size ≈ 5 — Indian urban average.
· ~50% of Delhi households own a car — Delhi is India's most car-dense large city, well above the ~10% national urban average.
· Car-owning households average ~1.25 cars — a meaningful minority own two.
· Commercial fleet (taxis, cabs, corporate) adds ~0.5M cars on top of private ownership.
· Red ≈ 5% of the colour mix — white/silver/grey dominate Indian car sales (~70% combined); red is a distinct-minority choice.

The worked solution

Households in Delhi

20M ÷ 5 per household = 4M households

Car-owning households

4M × 50% = 2M households

Private cars

2M × 1.25 cars each = 2.5M cars

Add commercial/taxi fleet

2.5M + 0.5M = 3M cars on the road

Apply red colour share

3M × 5% = 150,000 red cars

Households

Base20M people

Filter / rate÷ 5

Result4M

Car-owning households

Base4M

Filter / rate× 50%

Result2M

Private cars

Base2M

Filter / rate× 1.25 cars/HH

Result2.5M

Total cars incl. commercial

Base2.5M

Filter / rate+ 0.5M fleet

Result3M

Red cars

Base3M

Filter / rate× 5% red share

Result≈ 1.5 lakh

Answer

≈ 1.5 lakh red cars

Full calculation

Step	Base	Filter / rate	Result
Households	20M people	÷ 5	4M
Car-owning households	4M	× 50%	2M
Private cars	2M	× 1.25 cars/HH	2.5M
Total cars incl. commercial	2.5M	+ 0.5M fleet	3M
Red cars	3M	× 5% red share	≈ 1.5 lakh

Sanity check

Delhi's transport department counts ~3.3M registered cars on the road — our 3M base is right on it. And red at 5% is defensible given white alone is ~35–40% of Indian car sales; even doubling red's share only moves the answer to 3 lakh, same order of magnitude.

The lesson to carry

Attribute questions = (population of objects) × (attribute share). Nail the base count first; the colour percentage is a one-line judgment call the interviewer just wants you to bound sensibly.

Attempt it before you peek

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