Venture Capital puzzles, solved step by step

About 381 companies a year. The four pass rates multiply to 0.525%, so only one sourced company in about 190 becomes a closed deal. Working backwards: 2 deals need 2.86 term sheets, 19 partner meetings and 76 first meetings, which need 381 companies in the top of the funnel. That is seven or eight new companies every week of the year.

Why do the pass rates multiply?

Think of a college admission that needs you to clear a written test, then an interview, then a document check. If one applicant in five clears the test and one in four of those clears the interview, only one in twenty of the original applicants is still standing before the document check even starts. Each stage of a funnel acts only on what survived the stage before it, so the overall rate is the product of the stage rates, not their sum or average. Here that product is 0.20 x 0.25 x 0.15 x 0.70, which is 0.00525, or about one company in 190.

How do you say it out loud without losing the room?

Work backwards from the answer the interviewer cares about, one stage at a time, and say each number as you go. Two closed deals at a 70% close rate need 2.86 term sheets; at 15% that is 19 partner meetings; at 25% that is 76 first meetings; at 20% that is 381 companies. Then translate it into a working week: 381 over 52 is about 7.3 new companies a week and about one and a half first meetings a week, which is a concrete picture of the job.

Keep the fractions until the end. If you round up at every stage instead, you get 3 term sheets, 20 partner meetings, 80 first meetings and 400 companies, a 5% overshoot from rounding alone. It is not a disaster, but it shows the interviewer you carry precision until the last step.

What would you add after the number?

Point at the stage with the most leverage. Every rate matters equally in the product, but they are not equally easy to move. Lifting the partner-meeting rate from 25% to 35%, by screening harder before first meetings, cuts the sourcing need to about 272 companies. The limitation is worth a sentence too: real funnels are lumpy, and a fund that closes two deals a year will see years with one and years with four.

About 1 crore weddings a year, within a range of roughly 85 lakh to 1.14 crore. Assume about 140 crore people spread over about 70 years of age, so about 2 crore per year of age, nudged up to 2.2 crore because India skews young. If 90% of them marry, 1.98 crore people marry each year, and two people per wedding gives about 99 lakh weddings.

Why start from one age cohort?

A school counting how many students graduate each year does not start from every student on its rolls; it counts one class, because each class graduates once. Weddings are a yearly flow, and each person typically marries once, so the yearly number of weddings is set by how many people reach marriage age in a year, not by the size of the population. If 140 crore people are spread across roughly 70 years of age, each single year of age holds about 2 crore people. India's population skews young, so the cohorts now reaching their twenties are larger than that average; 2.2 crore is a reasonable working figure.

How confident can you be, and how do you show it?

Give a range by moving the two softest assumptions. With a cohort between 2.0 and 2.4 crore and between 85% and 95% of people marrying, the answer runs from about 85 lakh to 1.14 crore weddings a year, so 1 crore is a sound central figure. The population input is an assumption to confirm against the latest census or official estimate. Remarriages and people who marry abroad move the answer by a few percent at most.

What does an investor do with the number?

Narrow it to the startup's real market. A wedding-services company does not serve every wedding; it serves the urban weddings with a budget above some level, in cities where it operates. Say which cut you would apply next, for example the share of weddings in the top cities and above a spend threshold, and what you would multiply by to reach a rupee market size. That shows you know the count is the first step of a market sizing, not the answer.

About Rs 144 crore a year. Three lakh dentists at two per clinic is 1,50,000 clinics. Forty per cent of those, the city clinics likely to buy software, is 60,000. At Rs 24,000 a year each, that is Rs 144 crore. The figure most open to challenge is dentists per clinic: at three per clinic the market is Rs 96 crore, at one and a half it is Rs 192 crore.

Why start by turning dentists into clinics?

If you were sizing the market for kitchen ovens you would count kitchens, not cooks, because a house with four cooks still buys one oven. A market is counted in the unit that pays, and practice-management software is bought once per clinic, so the first step converts people into paying units. Three lakh dentists at two per clinic gives 1,50,000 clinics. Skip the step and you double the answer before you have made a single judgement.

Which assumption would a partner push on first?

Rank the steps by how wrong they could be. The dentist count comes from a register and is unlikely to be far off. Dentists per clinic is the step to defend, because many dentists practise alone while others work across two or three clinics, and the answer moves in proportion to it. At three per clinic the market is Rs 96 crore; at one and a half it is Rs 192 crore. The price is next: Rs 24,000 a year is Rs 2,000 a month, which a solo clinic may resist and a multi-chair chain may pay several times over.

What exactly does Rs 144 crore measure?

Be precise about the label. The 40% filter removes clinics unlikely to buy, so this is closer to a serviceable market than to the total, and it assumes every likely buyer pays full price to someone. It is the size of the prize across all vendors, not the revenue one startup can expect, and a fund will ask what share is winnable and how quickly. State the limitation plainly: every input here is an assumption to verify, the dentist count against the current professional register in particular, before the number goes into an investment memo.

About Rs 1,296 crore a year of packaged pet food spend, of which a brand winning 5% would take about Rs 65 crore. Take 2.5 crore households in the eight cities, 12% owning a dog or cat, 30% of those buying packaged food, and Rs 1,200 a month, or Rs 14,400 a year, per buying household. That is 9 lakh households and about Rs 1,296 crore. Pet ownership and the packaged share are the two numbers to defend.

How do you build the tree so each step can be challenged?

Sizing a market is like estimating how many people in your building would join a weekend cricket league: count the flats, then the ones with a player, then the ones who would pay a fee. Each branch should be one filter you can name and defend separately, so a challenge to one number does not bring down the whole estimate. Here the branches are households, pet ownership, packaged-food use and spend. Every figure is an assumption to check against current survey data before it goes into a memo; the point in the room is the structure.

Which assumptions move the answer most?

Give each assumption a plausible range and move one at a time. Pet ownership from 8% to 16% and the packaged share from 20% to 40% each swing the answer from Rs 864 crore to Rs 1,728 crore, wider than either spend or household count. Spend from Rs 900 to Rs 1,500 a month moves it only to Rs 972 crore and Rs 1,620 crore, and the household count is the best known of the four. So the diligence effort goes on ownership and packaged share, and a founder's deck that is vague on those two is vague where it matters.

How do you get from the market to one brand's revenue?

The Rs 1,296 crore is spend across every brand and channel, including shops. A direct-to-consumer brand's potential is a share of that pool, and at 5% it would be about Rs 65 crore a year, which is the number to compare with the round size. State the limits: the packaged share is growing, so today's figure understates the pool in five years; and the estimate ignores smaller pets, treats and accessories, which a brand may sell alongside food.

About Rs 324 crore a year. Start with 1.2 crore stores. 15% sell more than Rs 20,000 a day, which leaves 18 lakh stores busy enough to need billing software. 30% of those will pay, which leaves 5.4 lakh paying stores. At Rs 500 a month, or Rs 6,000 a year, that is Rs 324 crore. The Rs 7,200 crore you get by charging every store is the total market, not the one this app can serve.

Why not multiply every kirana store by the price?

A tailor opening a shop in a colony of 2,000 homes does not have 2,000 customers. He has the homes that buy stitched clothes, at his prices, from a shop, rather than from a relative with a machine. A serviceable market counts only the buyers who feel the problem badly enough to pay for the fix, so every filter must describe a real reason a store would or would not buy. The Rs 20,000 daily sales cut is that reason here: a store taking in that much has enough bills, credit customers and stock lines that paper billing starts to hurt. Multiply all 1.2 crore stores by Rs 6,000 and you get Rs 7,200 crore, the total addressable marketRevenue if every possible buyer in the category bought the product at its price. A ceiling, rarely a plan., which describes the country rather than this app.

How do you say the answer so it survives the follow-up?

Say the chain as three multiplications and carry the unit at every step: stores, then stores, then rupees. The most common slip in this question is mixing a monthly price with an annual market, so say both numbers out loud: Rs 27 crore a month, Rs 324 crore a year. Then name the weakest link yourself. The 30% willingness to pay is the least grounded figure, and the answer moves one for one with it: at 20% the market is Rs 216 crore, at 40% it is Rs 432 crore.

Finish with what the number does and does not tell an investor. Rs 324 crore is a ceiling on this product's revenue, not a forecast; the app would win some share of the 5.4 lakh stores, and competitors are chasing the same ones. A partner hearing this will ask two things: what share is realistic in five years, and whether the stores can be sold a second product, such as working capital credit, that makes the market bigger than billing alone. The 1.2 crore store count is the question's premise; outside the room, confirm it against a published retail survey before building on it.

Roughly 35,000 to 50,000 trucks a day, call it 40,000. From the goods: about 3 crore people, each accounting for some 10 kg of goods leaving the region daily, gives 3 lakh tonnes; at 12 tonnes a truck that is 25,000 loaded trucks, or about 35,714 once empty departures are added. From the trucks: about 4 lakh trucks serving NCR, each leaving once every 8 days, gives 50,000. Two routes within 1.4x of each other make the range defensible.

Why build the number twice?

A carpenter measures twice before cutting, not because the first measurement was careless but because a second, separate measurement catches the slip the first one hid. An estimate built from one chain of assumptions can be precise and still out by ten times; a second route built from different assumptions is the only check you can run in the room. Here the first route starts from what has to move, goods, and the second from what moves it, trucks. They share no inputs, so their agreement means something.

Walk route A slowly. Assume about 3 crore people in NCR. Outbound freight is the manufactured goods from the industrial belts plus wholesale trade re-sent to the rest of north India; assume 10 kg per resident a day, so 3 lakh tonnes. A loaded truck averages perhaps 12 tonnes across small and large vehicles, giving 25,000 loaded departures. Trucks that came in loaded often leave empty; if 30% of departures are empty, total departures are 25,000 divided by 0.7, about 35,714. Route B: assume 4 lakh intercity trucks, from NCR and outside, serve the region, and an average round trip takes 8 days, so 50,000 leave each day.

How would you check it outside the room?

The best check is a third, measured source: GST e-way bills, which are generated for goods moved above a value threshold and are published at state level, and toll plaza counts of goods vehicles on the main exits from NCR. Each has its own bias; e-way bills miss low-value loads and toll counts mix through traffic with NCR departures, so use them to test the range rather than replace it. A morning spent with brokers at a transport hub would test the 30% empty share and the 8-day trip, the two inputs most likely to be wrong.

Then say what the number is for. Trucks leaving a day is not the market; the marketplace earns on loads it matches. At 40,000 departures a day, if a third are booked through brokers and the platform takes a fee per load, the next step is the fee times the brokered loads. The truck count is the base everything else multiplies, which is why it deserves two routes.

About 7,000 buses, and about Rs 34 lakh a year at 10% share. Take 1.4 crore people; about 20% are of school age, 28 lakh children. Assume half attend schools that run buses, 14 lakh, and a quarter of those ride, 3.5 lakh. At about 50 riders a bus, that is 7,000 buses, in a range of roughly 4,667 to 10,500. Winning 700 of them at Rs 4,800 a year each is about Rs 33.6 lakh.

How do you build the count so each step can be challenged?

Planning a wedding, you do not guess the number of plates; you count families, then members per family, then how many will turn up. A sizing is only as good as its weakest stated assumption, so each step should be a single number with a reason the interviewer can push on. Here the chain is people, school-age children, children in schools that run buses, children who ride, and riders per bus. The 20% school-age share is the firmest; whether half of children attend schools that run buses is the least certain and depends on the city's mix of private and government schools.

What does the number tell an investor?

Give the range, then the judgement. Riders between 20% and 30% and buses carrying 40 to 60 riders give 4,667 to 10,500 buses, and revenue between about Rs 22 lakh and Rs 50 lakh a year. Even at the top of the range, one city at 10% share is a small business, so the case for investing rests on winning many cities, a higher share, or more revenue per bus, not on this city alone. A parent subscription for live tracking, or selling route planning and fuel tracking to the school, could change the revenue per bus more than any share assumption.

To check it outside the room, ask the transport department how many vehicles are registered as school buses in the city, since many states register them under a separate category, and call three or four large schools to ask how many buses they run per thousand students. Confirm the 20% school-age share against the latest census or survey for that city rather than taking it from memory.

About Rs 24,000 crore a year on these assumptions, and supply, not demand, sets the ceiling. Take 60 crore phones in use on a 4-year cycle: 15 crore retire each year. If 40% are resold and half of those are refurbished, 3 crore units reach the refurbished channel at about Rs 8,000 each. Every input is an assumption to check against market data.

Why start from the phones people retire rather than the people who want one?

A second-hand bookshop can only sell the books people give up. However many students want cheap textbooks, the shop's shelves fill at the rate books are released. A refurbished market is a used-goods market, so its volume is capped by the flow of retired devices before anyone asks about demand. Size the flow first, then check demand only to see whether it is large enough to absorb that flow.

How do you build and defend each step?

Say every number is an assumption and give the reason for its size. Installed base over replacement cycle gives the retiring flow: 60 crore over 4 years is 15 crore phones a year. Of those, many stay in a drawer or pass to a parent, so assume 40% are sold or traded in, 6 crore. Some go straight to a buyer as they are; assume half pass through a grading, repair and warranty channel, 3 crore units. At an average Rs 8,000, that is Rs 24,000 crore.

How do you show that supply rather than demand caps it?

Run a quick demand check. If about 18 crore phones are bought each year, new and used, and a quarter of buyers would take a refurbished phone at a fair price, demand is about 4.5 crore units, more than the 3 crore supply. When demand exceeds supply, the market is the supply, so the replacement cycle is the lever to test. A 3-year cycle lifts the flow to 20 crore retired phones and the market to Rs 32,000 crore, a bigger swing than any plausible change in price. That also tells an investor where the business is won: in sourcing devices, not in finding buyers.