Venture Capital puzzles, solved step by step

Puzzles: 100
Traced to a firm: 7
Topics: 12
Hard: 30

Showing 41–50 of 100

041Three co-founders own 50%, 30% and 20% of their company. The CTO owns more than the COO. The CEO does not own 30%. The COO does not own the least. Who owns what?Logic and brainteasersWarm upSeed and early-stage VCMulti-stage VC
Try it first
Which founder holds 50%?
Show the worked solution
The CTO owns 50%, the COO 30% and the CEO 20%. Start with the COO, the person two clues mention. Not owning the least rules out 20. The CTO owning more rules out 50, since nobody can own more than 50. So the COO holds 30, the CTO must hold the 50, and the CEO has the 20 left, which fits the clue that the CEO does not own 30.
Where should you start a puzzle like this?
Seating a dinner table works the same way: you begin with the guest who has the most constraints, because each rule about them removes options for everyone else. Start with the person the most clues mention, here the COO, since two clues bear on the COO and each one deletes a column. Not owning the least removes 20. The CTO owning more than the COO removes 50, because there is no larger stake for the CTO to hold. That leaves the COO at 30 before you have used the third clue.
The two clues about the COO cross out 20% and 50%, which fixes the COO at 30%; the CTO must then hold 50% and the CEO 20%, the only one of six possible assignments that passes every clue.
How do you know the answer is the only one?
There are only six ways to hand three stakes to three people, so you can check them all, but the grid makes it quicker. Once the COO is fixed at 30, the relational clue forces the CTO into the one stake larger than 30, and the last stake goes to the CEO by elimination. Then use the clue you have not used yet as a check: the CEO holds 20, not 30, so it is satisfied. A clue that was never needed to find the answer but still holds is good evidence you have not made a slip.
Say the method as you go. An interviewer giving a one-minute logic puzzle is listening for an order of reasoning, not just the answer, so name which clue you use at each step. The trap is to start with the CEO, because the CEO is listed first, and then guess. One clue about the CEO removes only one cell, so you are left trying cases.
Why would a venture interviewer ask a founders' puzzle?
It is a warm-up that tests clean reasoning under mild time pressure, dressed in the language of a cap table. It also hints at something real: founder splits rarely follow titles, and an investor reading a cap table should not assume the CEO holds the largest stake. The limitation is obvious: real ownership questions are settled by the share register and the shareholders' agreement, not by inference, and the useful skill here is the elimination habit, not the founders.
Where candidates lose it
The common loss is assuming the CEO holds the most and then trying to fit the clues around that. The CEO clue only says what the CEO does not own, and starting there leaves you guessing between two cases.
The second loss is reading the CTO clue as about the CEO, or forgetting that nobody can own more than 50, which is what rules the COO out of the top stake. Read each clue once, slowly, and cross out the cells it kills.
What the interviewer asks next
If the clue said the CTO owns less than the COO instead, who owns what?
Add a fourth founder and a 10% stake. What is the smallest number of clues that can fix every stake?
Which single clue could you drop and still get a unique answer?
042A mental maths set from a first-round interview: work out 49 x 51, 998 x 1,002 and 12.5% of Rs 3,680 crore, each inside ten seconds.Mental maths and speed testsWarm upGeneral AtlanticNew York · 2026
Try it first
What is 998 x 1,002?
Show the worked solution
2,499, then 9,99,996, then Rs 460 crore. The first two use the same shortcut: numbers equally spaced either side of a round number multiply to its square minus the gap squared, so 49 x 51 is 2,500 minus 1, and 998 x 1,002 is 10,00,000 minus 4. The third is a fraction in disguise: 12.5% is one eighth, so halve Rs 3,680 crore three times, to 1,840, 920 and 460.
Why does 49 x 51 come out one short of 2,500?
Picture a square garden 50 metres a side. Take a one-metre strip off the bottom, 50 square metres, and lay it along the right-hand side. It only fits for 49 metres, so one square metre is left over. A rectangle 49 by 51 is a 50 by 50 square with one corner square missing, so the product is 2,500 minus 1, or 2,499. The same picture works for any pair spread evenly around a round number: the product is the middle number squared minus the gap squared.
The relationship
$(a - b)(a + b) = a^2 - b^2 \qquad 49 \times 51 = 50^2 - 1^2 = 2{,}499 \qquad 998 \times 1{,}002 = 1{,}000^2 - 2^2 = 9{,}99{,}996$
a the round number in the middle, 50 or 1,000
b how far each factor sits from it, 1 or 2
a squared minus b squared the product, always slightly below the square
What it says in wordsTwo numbers spread evenly either side of a round number multiply to that number squared, less the gap squared.
49 x 51 is a 50 by 50 square with one unit square missing, so it equals 2,499, and 12.5% of Rs 3,680 crore is one of eight equal blocks, Rs 460 crore, found by halving three times.
How do you take 12.5% of anything in a few seconds?
Recognise the fraction first. 12.5% is one eighth, and dividing by eight is the same as halving three times, which is easier to do aloud than any long division. Rs 3,680 crore halves to 1,840, then 920, then 460. Keep a short list of these anchors ready: 12.5% is an eighth, 37.5% three eighths, 16.7% a sixth, 6.25% a sixteenth. Interviewers who give percentage questions usually pick one of them, because the speed of recognising the fraction is what they are testing.
What is the interviewer actually checking?
Speed sets are less about arithmetic than about whether you look for structure before you calculate. Saying the shortcut out loud, square minus one, or halve three times, shows a method that will also work on the next question. Two habits help. Check the size of your answer against an anchor: 49 x 51 must sit just under 2,500. And say the number back with its units, Rs 460 crore, not just 460. The limit of these tricks is that they only work on numbers chosen to suit them; for awkward numbers, round and say so.
Where candidates lose it
The common loss on the products is grinding through long multiplication and running out of time, or writing 10,00,004 because the sign of the correction is guessed. The product of numbers either side of a round number is always below its square.
On the percentage, candidates multiply 3,680 by 0.125 digit by digit and fumble. Name the fraction, one eighth, and halve three times; the clock is part of the question.
What the interviewer asks next
Work out 97 x 103 and 4.95 x 5.05 the same way.
What is 37.5% of Rs 2,400 crore?
Estimate 1,999 squared in your head.
Asked at General Atlantic, Generalist, New York, 2026 (Wall Street Oasis): The first round was behavioral with mental math at the end.
043One investment returns 3x in 3 years. Another returns 5x in 7 years. Which has the higher IRR, and by how much?Growth and compoundingCoreGrowth equityFund of funds and LPs
Try it first
Which investment has the higher IRR?
Show the worked solution
The 3x in 3 years, at about 44.2% a year against 25.8%, a gap of about 18 points. IRR for a single cash in and out is the multiple's root over the years held. The cube root of 3 is about 1.44 because 1.44 cubed is 2.99. The seventh root of 5 is about 1.26 because 1.26 to the seventh is just over 5. Time sits under the multiple, so the smaller, quicker multiple earns the higher rate.
Why can a smaller multiple have the higher IRR?
Two runners: one covers 3 kilometres in 3 minutes, the other 5 kilometres in 7 minutes. The second went further, but the first was faster. A multiple says how far the money went; the IRR says how fast, so time sits in the denominator and a long hold drags the rate down. For a single cheque in and a single exit, the IRR is the yearly growth rate that turns 1 into the multiple over the holding period: the multiple's root over the years.
The relationship
$\text{IRR} = M^{1/t} - 1 \qquad 3^{1/3} - 1 \approx 44.2\% \qquad 5^{1/7} - 1 \approx 25.8\%$
M the money multiple, cash out divided by cash in
t the holding period in years
IRR the annual rate that grows 1 into M over t years
What it says in wordsThe annual rate is the multiple's root over the years held, less one.
The 3x deal climbs at 44.2% a year and the 5x deal at 25.8%, so the smaller multiple earns the higher rate; the 3x proceeds only need to grow at 13.6% a year afterwards to match 5x by year seven.
How do you take those roots without a calculator?
Guess and cube. 1.4 cubed is 2.744 and 1.5 cubed is 3.375, so the cube root of 3 is a little above 1.4; 1.44 cubed is 2.986, close enough, so 44%. For the seventh root of 5, use doublings: 5x is about 2.3 doublings, since 2 to the 2.3 is about 5, and 2.3 doublings in 7 years is one every 3 years, which the rule of 72 puts at about 24%. The rule of 72 runs a little low at rates this high, so nudge up: 1.26 to the seventh is just over 5, giving about 26%.
Does the higher IRR make the 3x the better investment?
Not on its own. The 3x deal wins on rate, but it hands money back after three years, and whether that is better depends on what the money can earn next. To match 5x over the same seven years, the 3x proceeds need to grow 5/3 times over the remaining four years, about 13.6% a year. If the fund or its LPs can redeploy above that, the quick 3x is better; if not, the 5x leaves more money in total. This is why LPs look at both IRR and multiple: a high IRR on a short hold can return fewer rupees.
Where candidates lose it
The common loss is picking the 5x because 5 is bigger than 3, or dividing multiples by years, 1x a year against 0.71x a year, which gets the order right but the rates badly wrong.
The second loss is giving the IRRs and stopping. The interviewer often wants the follow-through: the higher IRR is not automatically the better deal, because the quicker exit has to be reinvested, and the break-even redeployment rate of about 13.6% settles it.
What the interviewer asks next
What multiple over 7 years matches a 44.2% IRR?
If the 3x deal had a two-year delay between investment and the first rupee of value, how would its IRR change?
Why might a fund that reports a high IRR still have a low multiple, and which number should an LP trust more?

044Estimate the annual revenue potential for a direct-to-consumer pet food brand in India's eight largest cities. State each assumption for households, pet ownership, packaged-food use and spend.Market sizing and estimationCoreConsumer internet VCIndia VC

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With 2.5 crore households, 12% owning a dog or cat, 30% of those buying packaged food and Rs 1,200 a month of spend, what is the market?

Show the worked solution

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.

The tree runs from 2.5 crore households to 9 lakh packaged-food buyers and about Rs 1,296 crore a year, and the sensitivity bars show pet ownership and the packaged share each moving the answer between Rs 864 crore and Rs 1,728 crore.

The relationship

\text{market} = 2.5\text{ cr} \times 0.12 \times 0.30 \times 14{,}400 = 9\text{ lakh} \times 14{,}400 \approx \text{Rs } 1{,}296 \text{ crore}

2.5 cr	households in the eight largest cities, an assumption
0.12	share of households with a dog or cat
0.30	share of pet households buying packaged food rather than home-cooked
14,400	annual spend per buying household, Rs 1,200 a month

What it says in wordsHouseholds, filtered twice, times what each buying household spends in a year.

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.

Where candidates lose it

The common loss is a number with no visible structure, such as a single guess of the pet population times a price. The interviewer cannot challenge a step that was never stated, and will mark you down for that rather than for the number.

The second loss is mixing monthly and annual spend, or forgetting the packaged-food filter, and ending a factor of three or twelve away. Say the units at every step and annualise once, at the end.

What the interviewer asks next

How would you check the pet ownership figure quickly and cheaply?
What share of this market would the brand need to justify a Rs 100 crore post-money valuation at 4x revenue?
How would you size the same market from the supply side, starting with manufacturers?

045Investor A is right 40% of the time, and each winner returns 3x. Investor B is right 10% of the time, and each winner returns 25x. Losers return 0.2x for both. Whose portfolio returns more?Power law and portfolio mathsWarm upSeed and early-stage VCSeries A to C VC
Try it first
What does each portfolio return per rupee, on average?
Show the worked solution
Investor B, at 2.68x against 1.32x. Expected multiple is each outcome times its chance. A gets 0.4 x 3 from winners and 0.6 x 0.2 from losers, 1.32x. B gets 0.1 x 25 and 0.9 x 0.2, 2.68x. B is wrong nine times in ten but its winners are big enough to carry the portfolio; A's winners need to be 6.4x to draw level.
Why does the investor who is usually wrong do better?
A shopkeeper who makes a small profit on four sales in ten and a small loss on the rest earns steadily but slowly. A fisherman who comes back empty nine days in ten but lands one huge catch on the tenth can still earn far more. In venture the size of the winners matters more than how often you win, because losses are capped at the cheque while winners are not. A's high hit rate buys only 1.20x from winners; B's one-in-ten rate buys 2.50x.
The relationship
$E[M] = p \, W + (1 - p) \, L \qquad A: 0.4 \times 3 + 0.6 \times 0.2 = 1.32 \qquad B: 0.1 \times 25 + 0.9 \times 0.2 = 2.68$
p the hit rate, the share of investments that win
W the multiple a winner returns
L the multiple a loser returns, 0.2x for both investors
What it says in wordsWeight the winners' multiple by the hit rate and the losers' by the miss rate, and add.
Investor A's winners contribute 1.20x and B's contribute 2.50x, so B's portfolio returns 2.68x against A's 1.32x even though B is wrong nine times in ten.
How far would either number have to move to flip the answer?
Solve for the break-even, because it tells you how robust the answer is. A's winners would need to return 6.4x, more than twice their 3x, to draw level, while B's hit rate could fall from 10% to 4.5% before B dropped to A's 1.32x. B's lead survives a large error in its hit rate, which is why venture investors talk about the size of possible outcomes before the chance of success: an investment that cannot return 25x cannot carry a portfolio like this.
What does the average hide about investor B?
Variance. With 20 investments and a 10% hit rate, B finds no winner at all 12% of the time and returns 0.2x. One winner is enough to lift B's 20-company portfolio to 1.44x, above A's expected 1.32x, so B's result depends heavily on whether it lands at least one outlier. That is the case for venture portfolios of 25 or more companies, and the limitation of the clean comparison: a fund with too few bets can follow B's strategy correctly and still lose money.
Where candidates lose it
The common loss is picking A because 40% sounds like a much better investor than 10%. Hit rate is half the calculation; the other half is how much each win returns, and in venture that half usually dominates.
The second loss is forgetting the losers' 0.2x and answering 1.20x and 2.50x. The order is right but the numbers are wrong, and the interviewer asked for the portfolio return.
What the interviewer asks next
How many investments does B need for at least a 95% chance of one or more winners?
If B's winners return 15x instead of 25x, who wins now?
Why might a later-stage fund deliberately run A's strategy?
046A software company offers a monthly plan at price p with 4% monthly churn, or an annual plan paid upfront at a 20% discount. Which brings in more revenue per customer in the first year?SaaS and unit economics riddlesCoreSaaS-focused VCSeed and early-stage VC
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Over the first year, how does expected revenue per customer compare?
Show the worked solution
They are almost equal: about 9.68p a year on the monthly plan against 9.6p on the annual plan. The monthly customer pays p in month one and is still paying with probability 0.96 to the k in month k plus one, so twelve months add to about 9.68p. The annual customer pays 12 x 0.8p, 9.6p, upfront. With revenue a near tie, the cash on day one and the lower churn of a committed customer decide it for annual.
How do you count revenue from a customer who might leave?
A gym that sells monthly memberships cannot count on twelve payments from every member who joins in January, because some stop coming in March. Expected revenue from a monthly customer is each month's price times the chance they are still a customer that month, added up. With 4% churn, the chance of still paying in month k plus one is 0.96 to the k: 1 in the first month, 0.96 in the second, and 0.61 by the twelfth. Twelve terms of a shrinking series add to about 9.68p, not 12p.
The relationship
$\sum_{k=0}^{11} 0.96^{k} \, p = \frac{1 - 0.96^{12}}{0.04}\, p \approx 9.68p \qquad 12 \times 0.8p = 9.6p$
p the monthly list price
0.96 the chance a customer stays from one month to the next
0.8p the discounted monthly price on the annual plan
What it says in wordsA year of monthly revenue is a shrinking series of payments; the annual plan is twelve discounted payments collected at once.
A monthly customer's expected payments shrink from p to 0.64p over the year and add to 9.68p, almost the same as the 9.6p an annual customer pays upfront, so the revenue difference is under 1%.
If revenue is a near tie, what decides it?
Everything the revenue sum leaves out. The annual plan collects 9.6p on day one, which funds growth without new equity, while the monthly plan collects its 9.68p over twelve months. Annual customers also cannot churn mid-year, and at renewal they tend to churn less than monthly customers, so year two favours annual too. The break-even is close: at monthly churn of 4.16% the two plans give the same first-year revenue, so at any churn above that the annual plan wins on revenue as well.
What could make the comparison misleading?
The sum assumes the same customer would choose either plan. In practice the customers who pick annual plans are already the more committed ones, so their lower churn is partly selection, not a result of the plan. A founder who shows that annual customers churn less is showing a correlation; the useful question is what happens to churn when the company pushes hesitant customers onto annual terms. The other limit is the discount itself: at 20% it is roughly break-even, but a deeper discount gives revenue away for cash that may be cheaper to raise elsewhere.
Where candidates lose it
The common loss is comparing 12p with 9.6p and declaring the monthly plan 25% better, as if no one churned. The question gave you the churn rate so that you would weight each month's payment by the chance the customer is still there.
The second loss is getting the near tie and stopping. The interviewer wants the tie-breakers: cash upfront, no mid-year churn, and the selection effect that flatters annual customers.
What the interviewer asks next
At what discount would the annual plan bring in exactly the same first-year revenue at 4% churn?
How would you compare the two plans over three years rather than one?
Why might a company report annual contracts as better retention when it is partly selection?
047A debt-free company has an enterprise value of Rs 1,000 crore and 10 crore shares at Rs 100. It borrows Rs 100 crore and buys back shares at Rs 125. Ignoring taxes, what happens to enterprise value, equity value and the price of the remaining shares, compared with a buyback at Rs 100?Valuation riddlesHardSilver LakeSan Francisco · 2022
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After the buyback at Rs 125, what is each remaining share worth?
Show the worked solution
Enterprise value stays at Rs 1,000 crore, equity value falls to Rs 900 crore, and the remaining shares fall to Rs 97.83, against Rs 100 for a buyback at Rs 100. Borrowing Rs 100 crore and paying it out swaps equity for debt without changing what the business is worth. At Rs 100 a share the company retires 1 crore shares and the price holds. At Rs 125 it retires only 0.8 crore, so the Rs 20 crore premium comes out of the holders who stay.
Why does enterprise value not change?
A house worth Rs 1 crore is still worth Rs 1 crore after the owner takes out a Rs 10 lakh loan against it and spends the cash; what changes is how much of the house the owner owns outright. Enterprise value is the value of the business, and borrowing to pay shareholders changes who has a claim on it, not what it is worth. The Rs 100 crore of new debt is matched by Rs 100 crore leaving the company, so net debt rises by Rs 100 crore and equity value falls by the same amount, to Rs 900 crore. That holds only while we ignore taxes and the costs of financial distress.
Enterprise value stays at Rs 1,000 crore while Rs 100 crore of it moves from equity to debt, and the price of each remaining share holds at Rs 100 for a buyback at Rs 100 but falls to Rs 97.83 for a buyback at Rs 125.
Why does the buyback price change the price per share?
Equity is Rs 900 crore after the buyback either way; what differs is how many shares it is split across. Buying at the fair price of Rs 100 retires 1 crore shares and leaves Rs 900 crore over 9 crore shares, Rs 100 a share, so nobody gains or loses. Paying Rs 125 retires only 0.8 crore shares, leaving Rs 900 crore over 9.2 crore, Rs 97.83. The sellers received Rs 100 crore for shares worth Rs 80 crore, a Rs 20 crore premium, and the holders who stay paid it: 9.2 crore shares times Rs 2.17 is Rs 20 crore.
The relationship
$P_{\text{after}} = \frac{EV - D}{N - D/P_{bb}} = \frac{1{,}000 - 100}{10 - 100/125} = \frac{900}{9.2} = 97.83$
EV enterprise value, Rs 1,000 crore, unchanged
D the new debt, Rs 100 crore, all paid out
N shares before the buyback, 10 crore
P bb the buyback price per share
What it says in wordsThe remaining equity is enterprise value less the new debt, spread over the shares not bought back.
What changes once you stop ignoring taxes?
Say the limits, because the interviewer will raise them next. Interest is usually tax-deductible, so the debt creates a tax saving that can lift enterprise value a little above Rs 1,000 crore; against that, more debt raises the risk and cost of distress. Signalling matters too: a buyback can tell the market that management thinks the shares are cheap, which may move the price on its own. None of that changes the core point. A buyback at a premium to fair value moves wealth from holders who stay to holders who sell.
Where candidates lose it
The common loss is saying the share price rises because there are fewer shares, or that enterprise value falls because cash left the company. The cash leaving is matched by debt arriving, so EV is unchanged, and fewer shares are matched by less equity.
The second loss is answering only the Rs 100 case. The question's Rs 125 is there to test whether you see that overpaying for shares hands the Rs 20 crore premium to sellers, and the remaining shares fall to Rs 97.83.
What the interviewer asks next
At what buyback price would the remaining shares rise above Rs 100?
With a 25% tax rate and permanent debt, roughly how much does the tax shield add to enterprise value?
How would the answer change if the company paid for the buyback from Rs 100 crore of existing cash instead of new debt?
Asked at Silver Lake, Technology, Media and Telecom, San Francisco, 2022 (Wall Street Oasis): If you raise $100 debt to buy back $100 of shares, how does that affect EV and equity value?
048A Rs 500 crore fund charges 2% a year on commitments for its first five years and 1.5% for the next five. How much is left to invest, and what gross multiple on invested capital does the portfolio need just to hand LPs their money back?Fund economics riddlesCoreFund of funds and LPsSeed and early-stage VC
Try it first
What gross multiple on invested capital returns exactly Rs 500 crore to LPs?
Show the worked solution
Rs 412.5 crore is left to invest, and the portfolio needs about 1.21x gross just to return the Rs 500 crore. Fees are 2% for five years, Rs 50 crore, plus 1.5% for five years, Rs 37.5 crore, a total of Rs 87.5 crore. LPs committed Rs 500 crore, so the Rs 412.5 crore that is invested must grow to Rs 500 crore: 500 over 412.5 is 1.21x before the fund earns a rupee of carry.
Why does a fund need more than 1x just to break even?
If a friend takes Rs 17.5 from every Rs 100 you give him to invest, the Rs 82.5 he does invest has to grow by a fifth just to give you your Rs 100 back. Management fees come out of commitments, so the portfolio is smaller than the money LPs put in, and it must earn the fees back before LPs see any profit. On a Rs 500 crore fund, ten years of fees at these rates take Rs 87.5 crore, 17.5% of the fund.
Rs 87.5 crore of fees leaves Rs 412.5 crore to invest, so the portfolio must make 1.21x just to return the Rs 500 crore committed, and about 2.73x to hand LPs 2x after carry.
The relationship
$\text{fees} = 500 \times (0.02 \times 5 + 0.015 \times 5) = 87.5 \qquad \text{gross to return capital} = \frac{500}{500 - 87.5} = \frac{500}{412.5} \approx 1.21x$
500 commitments, in Rs crore
0.02, 0.015 the yearly fee rates in the two periods
412.5 the capital actually invested after fees
What it says in wordsTotal the fees over the fund's life, subtract them from commitments, and divide what LPs put in by what was invested.
What multiple does the fund need to deliver a good result to LPs?
Run the same logic to a target. Say LPs want 2x net, Rs 1,000 crore, and the manager takes 20% carry on profit above the Rs 500 crore committed. The LPs' Rs 500 crore of profit is 80% of the total profit, so total profit must be Rs 625 crore and proceeds Rs 1,125 crore. That is 2.73x on the Rs 412.5 crore invested, so a 2x net fund is close to a 2.7x gross portfolio. The gap between gross and net is why LPs ask for both numbers and never compare one manager's gross with another's net.
Where does the clean answer go wrong in practice?
Funds often recycle: they reinvest early exit proceeds up to the amount of fees paid, so invested capital can approach the full Rs 500 crore and the break-even multiple falls towards 1x. The fee terms, the recycling allowance and the carry structure are set in each fund's limited partnership agreement, so confirm them there before using these figures for a real fund. Some funds also charge the later-period fee on invested capital rather than commitments, which lowers total fees.
Where candidates lose it
The common loss is saying 1x, or adding the fee percentage to 1 and answering about 1.18x. The fees shrink the base the return is earned on, so the break-even multiple is commitments divided by invested capital, 1.21x.
The second loss is computing fees as 2% for all ten years, Rs 100 crore, and missing the step-down. Read the fee schedule as the question gives it; the second five years are cheaper.
What the interviewer asks next
If the fund recycles Rs 50 crore of early proceeds, what gross multiple does it need to return capital?
What gross multiple delivers 3x net with 20% carry?
Why do larger funds usually charge lower fee rates, and what does that do to this calculation?
049Investors hold 40% of a company and Rs 150 crore of 1x non-participating preferences. The founders hold 50% and employees 10%. The company sells for Rs 160 crore. What do the founders receive?Preferences, payouts and protectionsHardSeries A to C VCIndia VC
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How much of the Rs 160 crore do the founders take home?
Show the worked solution
About Rs 8.33 crore, roughly 5% of the sale, although they own half the company. The investors compare their Rs 150 crore preference with 40% of Rs 160 crore, Rs 64 crore, and take the preference. That leaves Rs 10 crore for common shareholders. Founders hold 50 of the 60 points of common, so they get five sixths of Rs 10 crore, and employees get Rs 1.67 crore.
Why do founders who own half the company get so little?
If you own half a house with a large loan against it and sell it for slightly more than the loan, the bank is paid first and your half of the small remainder is all you get. A liquidation preference works like that loan: investors are paid their Rs 150 crore before common shareholders see anything, so in a sale close to the preference, ownership percentages barely matter. This is the preference overhangThe total of liquidation preferences ahead of common shareholders. Until a sale exceeds it by a wide margin, common holders receive little, whatever their ownership. founders worry about after raising a lot of money at high valuations.
Investors take their Rs 150 crore preference from the Rs 160 crore sale because converting would give them only Rs 64 crore, so the founders, who own half the company, receive Rs 8.33 crore, about 5% of the price.
The relationship
$\text{investors} = \max(150,\; 0.40 \times 160) = 150 \qquad \text{founders} = (160 - 150) \times \frac{50}{50 + 10} = 8.33$
150 the investors' 1x preference, in Rs crore
0.40 x 160 what investors would get by converting to common, Rs 64 crore
50 / (50 + 10) the founders' share of the common stock alone
What it says in wordsInvestors take the better of their preference and their converted share; whatever is left is split among the common holders only.
At what sale price does ownership start to matter again?
Investors convert when 40% of the sale beats Rs 150 crore, which happens above Rs 375 crore. Between Rs 150 crore and Rs 375 crore every extra rupee goes to common, so founders get five sixths of each rupee; above Rs 375 crore everyone shares by ownership and founders get half. At exactly Rs 375 crore the two rules give the same answer: founders take five sixths of Rs 225 crore, Rs 187.5 crore, which is half the sale. That is the price at which the founders' 50% stake finally means 50% of the money.
What does this mean for an investor sitting on the board?
A founder team facing Rs 8 crore from a Rs 160 crore sale has little reason to work for it, and a board that needs the founders to close the deal has a problem. That is why sales near the preference overhang often include a management carve-out, a slice of proceeds set aside for the team ahead of or alongside the preferences. The limits of the clean answer: real stacks have several series with different seniority, and any carve-out, transaction costs or debt come off the top first, which leaves common with even less.
Where candidates lose it
The common loss is answering Rs 80 crore, half the sale, as if preferences did not exist, or forcing the investors to convert. Non-participating investors choose the better of the two, and here the preference wins by a wide margin.
The second loss is splitting the Rs 10 crore by whole-company stakes, giving founders Rs 5 crore. After the investors take their preference, only common shares are left, and founders hold five sixths of those.
What the interviewer asks next
What would the founders receive if the preferences were participating?
How large a management carve-out would give the founders Rs 25 crore at this price?
At what sale price do the founders receive exactly Rs 50 crore?
050Two portfolio companies each have a 20% chance of failing this year. What is the chance that at least one fails if the failures are independent, if they are perfectly correlated, and if the chance both fail is 10%?Probability and expected valueCoreMulti-stage VCFund of funds and LPs
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If the failures are independent, what is the chance at least one company fails?
Show the worked solution
36% if independent, 20% if perfectly correlated, and 30% if the chance both fail is 10%. In each case the chance of at least one failure is 20% plus 20% minus the chance both fail. Independent failures overlap 0.2 x 0.2 = 4%, giving 36%. Perfectly correlated failures overlap completely, 20%, giving 20%. With a 10% overlap the answer is 30%. Correlation makes any failure less likely but both failing far more likely.
Why can you not just add the two chances?
Think of two friends who each forget your birthday one year in five. If you add the chances you get two in five, but that counts the years when both forget twice, once for each friend. The chance of at least one event is the sum of the two chances minus the chance both happen, so the overlap decides the answer. For two independent events the overlap is the product, 0.2 x 0.2 = 4%, and the answer is 36%. The complement route checks it: neither fails with chance 0.8 x 0.8 = 64%.
The relationship
$P(A \cup B) = P(A) + P(B) - P(A \cap B) \qquad 0.2 + 0.2 - 0.04 = 0.36 \qquad 0.4 - 0.10 = 0.30 \qquad 0.4 - 0.20 = 0.20$
P(A), P(B) each company's chance of failing, 20%
P(A and B) the chance both fail, which depends on how the failures are linked
P(A or B) the chance at least one fails
What it says in wordsAdd the two chances and subtract the overlap once, because the overlap was counted in both.
As the overlap between two 20% failure chances grows from 4% to 10% to 20%, the chance that at least one company fails falls from 36% to 30% to 20%, while the chance that both fail rises fivefold.
What does correlation do to a venture portfolio?
It trades many small surprises for fewer, larger ones. As failures become more correlated, the chance of at least one failure falls from 36% to 20%, but the chance both fail rises from 4% to 20%, five times higher. The 10% case corresponds to a correlation of about 0.37 between the two failure events. A fund full of companies selling to the same customers, or depending on the same funding market, looks diversified by count but behaves like fewer, bigger bets.
Why would an LP care about this more than a single fund manager?
An LP holding several funds cares about how many bad outcomes can arrive at once. Correlated failures are what turn an ordinary bad year into a vintage where most companies struggle together, and an average-case model that treats failures as independent understates that risk. The limitation is that correlation is hard to measure for private companies with few data points; in practice investors judge it from shared exposures, such as the same sector, the same customers or the same reliance on new funding, rather than from a computed number.
Where candidates lose it
The common loss is answering 40% for the independent case by adding the two chances. That double-counts the 4% where both fail, and the interviewer is listening for the subtraction or the complement.
The second loss is thinking correlation makes failure more likely across the board. It makes at least one failure less likely and both failing more likely, and the interesting answer says both halves.
What the interviewer asks next
With ten independent companies at 20% each, what is the chance at least one fails?
What is the largest possible chance that at least one of the two fails, and what overlap gives it?
How would you estimate correlation between two private portfolio companies with no price data?

a	the round number in the middle, 50 or 1,000
b	how far each factor sits from it, 1 or 2
a squared minus b squared	the product, always slightly below the square

M	the money multiple, cash out divided by cash in
t	the holding period in years
IRR	the annual rate that grows 1 into M over t years

p	the hit rate, the share of investments that win
W	the multiple a winner returns
L	the multiple a loser returns, 0.2x for both investors

EV	enterprise value, Rs 1,000 crore, unchanged
D	the new debt, Rs 100 crore, all paid out
N	shares before the buyback, 10 crore
P bb	the buyback price per share

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Where should you start a puzzle like this?

How do you know the answer is the only one?

Why would a venture interviewer ask a founders' puzzle?

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What the interviewer asks next

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Why does 49 x 51 come out one short of 2,500?

How do you take 12.5% of anything in a few seconds?

What is the interviewer actually checking?

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Why can a smaller multiple have the higher IRR?

How do you take those roots without a calculator?

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Why does the investor who is usually wrong do better?

How far would either number have to move to flip the answer?

What does the average hide about investor B?

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How do you count revenue from a customer who might leave?

If revenue is a near tie, what decides it?

What could make the comparison misleading?

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Why does enterprise value not change?

Why does the buyback price change the price per share?

What changes once you stop ignoring taxes?

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Why does a fund need more than 1x just to break even?

What multiple does the fund need to deliver a good result to LPs?

Where does the clean answer go wrong in practice?

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Why do founders who own half the company get so little?

At what sale price does ownership start to matter again?

What does this mean for an investor sitting on the board?

Where candidates lose it

What the interviewer asks next

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Why can you not just add the two chances?

What does correlation do to a venture portfolio?

Why would an LP care about this more than a single fund manager?

Where candidates lose it

What the interviewer asks next