Equity Research puzzles, solved step by step

Puzzles: 100
Traced to a firm: 19
Topics: 11
Hard: 30

Topic

All topics Probability and brainteasers12 Expected value and decisions8 Market sizing and estimation12 Returns and compounding9 Valuation riddles12 Three statement riddles10 EPS and share count9 Cost of capital and rates8 Growth, mix and unit economics8 Mental maths6 Data and reasoning traps6

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Any Warm up Core Hard

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Any Reported at a firm Standard

Showing 11–20 of 20 · filtered from 100Clear filters

065Money grows at 12% a year, compounded. Roughly how long does it take to double, and how long to grow eightfold?Returns and compoundingWarm upLong-only asset managementBuy-side equity research
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Answer inside ten seconds.
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About 6 years to double and about 18 years to grow eightfold. The rule of 72 says the doubling time is roughly 72 divided by the percentage rate, so 72 / 12 = 6 years; the exact figure is 6.1 years. Eightfold is three doublings, 2 x 2 x 2, so it takes three doubling times, about 18 years, and exactly 18.3. It is not eight times six.
Why does 72 divided by the rate work?
Think of a savings pot that earns 12% a year and never has anything taken out. Each year's interest earns interest the next year, so the pot grows faster in rupees every year while growing at the same percentage. The time to double depends only on the rate, and for everyday rates it is close to 72 divided by the rate in percent. The exact answer is the log of 2 over the log of 1.12, 6.12 years. The number 72 is used because it sits near the exact constant and divides neatly by 2, 3, 4, 6, 8, 9 and 12.
One rupee at 12% is worth 1.97 after 6 years, 3.90 after 12 and 7.69 after 18, so each six-year stretch roughly doubles the pot and eightfold takes about 18 years.
Why is eightfold 18 years and not 48?
Because growth multiplies. Eight is 2 x 2 x 2, so eightfold is three doublings, and each doubling takes the same six years whatever the size of the pot. The same counting gives the other useful anchors: fourfold is two doublings, 12 years; a thousandfold is about ten doublings, since 2 to the power 10 is 1,024, so about 60 years. Tenfold is a bit more than three doublings, exactly 20.3 years.
The relationship
$t_{2\times} \approx \frac{72}{12} = 6 \qquad t_{8\times} = 3 \times t_{2\times} \approx 18$
t_2x years to double
t_8x years to grow eightfold
72 the rule of 72 constant
12 the growth rate in percent
What it says in wordsDivide 72 by the rate for one doubling, then count how many doublings the target needs.
Rate Rule of 72 Exact doubling time
4% 18.0 years 17.67 years
8% 9.0 years 9.01 years
12% 6.0 years 6.12 years
18% 4.0 years 4.19 years
24% 3.0 years 3.22 years
The rule of 72 is almost exact near 8%, a little generous below it and increasingly short of the true doubling time as rates climb above 15%.
Where does an analyst use this?
Anywhere a growth rate needs to be turned into a sense of scale, fast. A company promising 24% growth is promising to double every three years; a fund charging 2% a year in fees gives up about a third of the pot over twenty years; inflation at 6% halves the value of money in about 12 years. Turning rates into doubling times is the quickest way to check whether a claim is plausible before any spreadsheet is opened.
Where candidates lose it
Eight times six, 48 years, is the whole trap. It treats compounding growth as if it added the same amount each year, which is exactly the straight-line instinct the question is designed to catch.
The quieter slip is presenting the rule as exact. Say about 6, a touch over 6 exactly, and you have shown you know the rule is an approximation that works best near 8%.
What the interviewer asks next
How long does it take to grow tenfold at 12%? (about 20 years)
At what rate does money double in five years?
Prices rise 6% a year. How long until the same basket costs twice as much?
071A timed aptitude item of the kind used on Wonderlic-style tests: if 3 analysts write 3 reports in 3 days, how many reports do 9 analysts write in 9 days?Data and reasoning trapsWarm upPoint72New York · 2026
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Answer inside ten seconds.
Show the worked solution
27 reports. Find the unit rate first: 3 analysts writing 3 reports in 3 days means one analyst writes one report in 3 days, a third of a report per analyst-day. Nine analysts working nine days put in 81 analyst-days, and 81 x 1/3 = 27. Tripling the team triples the output and tripling the time triples it again: 3 x 3 x 3 = 27.
Why does the fast answer of 9 feel right?
The sentence has a rhythm, three, three, three, then nine and nine, and the ear wants to finish the pattern with another nine. It is the same pull as a kitchen puzzle where three cooks bake three cakes in three hours. Matching the pattern of the words is the trap; the fix is to reduce the problem to one worker and one day before scaling anything. Once you have the rate per analyst-day, the answer is multiplication.
The question's case, 3 analysts for 3 days, is 9 analyst-days and 3 reports, so one report takes 3 analyst-days; the full 9 by 9 grid holds 81 analyst-days and therefore 27 reports.
How do you do it in ten seconds?
Scale each dimension on its own. Three times the analysts gives three times the reports, and three times the days gives three times again, so the answer is 3 reports x 3 x 3 = 27. The general rule is output equals the rate per worker per day, times the workers, times the days, and it handles any version of the item, including the ones where the numbers do not match so neatly.
The relationship
$\text{reports} = \frac{3}{3 \times 3} \times 9 \times 9 = \frac{1}{3} \times 81 = 27$
3 / (3 x 3) reports per analyst-day, one third
9 x 9 analyst-days in the new case, 81
What it says in wordsReports equal the rate per analyst-day times the number of analyst-days.
What is a timed test like this really checking?
Wonderlic-style tests put many short items against a tight clock, so the difficulty is the time, not any single item. The format, number of items and time allowed vary by version, so confirm what the firm uses. The habit that scores on the test is the same one that keeps a model right: write the unit rate, then scale it. On a timed test, skipping an item you cannot set up in a few seconds and coming back to it is usually worth more than grinding.
Where candidates lose it
Nine is the whole trap, and it comes from answering the rhythm of the sentence rather than the arithmetic. Under a clock, strong candidates say it because it sounds finished.
The second slip is 81, which is the number of analyst-days, not reports. Say the units out loud, reports per analyst-day, and both errors disappear.
What the interviewer asks next
If 5 machines make 5 widgets in 5 minutes, how long do 100 machines take to make 100 widgets?
Two analysts together write a report in 6 days; one alone takes 10. How long does the other take alone? (15 days)
How would you pace a timed test where finishing every item is not expected?
Asked at Point72, Investment Research, New York, 2026 (Wall Street Oasis): Final round was scheduled shortly after as well as a Wonderlic/Personality test.
072A car leaves point A for point B, 100 miles away, at 50 miles an hour. At the same moment a bird leaves B flying towards A at 100 miles an hour. Each time the bird meets the car it turns back to B, and each time it reaches B it turns towards the car again, until the car reaches B. How far does the bird fly?Probability and brainteasersWarm upBlackRockNew York · 2025
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How far does the bird fly?
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200 miles. Ignore the zigzag and ask how long the bird is in the air. The car takes 100 / 50 = 2 hours to reach B, and the bird flies the whole time at 100 miles an hour, so it covers 2 x 100 = 200 miles. Summing the legs gives the same answer: 133.3 miles in the first round trip, then a third as much each round, and 133.3 / (1 - 1/3) = 200.
What is the shortcut, and why does it work?
Picture walking home while your dog runs back and forth between you and the front door. Ask how far the dog ran and the back and forth looks like the hard part, but the dog simply ran at its own speed for exactly as long as your walk took. When something moves at a constant speed for a known time, the distance is speed times time, however many times it turns around. The car's trip fixes the time at 2 hours, and the bird's speed does the rest.
The bird's zigzag shrinks by a third with each round trip, starting at 133.3 miles, but it flies for exactly the car's 2 hours at 100 miles an hour, so its total is 200 miles either way you count.
How do you check it the long way?
The first meeting comes when the gap of 100 miles closes at 150 miles an hour, after 40 minutes, 33.3 miles from A. The bird has flown 66.7 miles and flies 66.7 back to B, a first round trip of 133.3 miles. By then the car is two thirds of the way, and every later round trip covers a third of the remaining gap, so each is a third of the last. A geometric series with first term 133.3 and ratio one third sums to 133.3 / (2/3) = 200, the same answer the shortcut gives in one line.
The relationship
$d_{bird} = v_{bird} \times t_{car} = 100 \times \frac{100}{50} = 200 \qquad \frac{133.3}{1 - 1/3} = 200$
v_bird the bird's speed, 100 miles an hour
t_car the car's travel time, 2 hours
133.3 the bird's first round trip in miles
1/3 the ratio of each round trip to the one before
What it says in wordsThe bird's distance is its speed times the car's travel time, and the geometric series of round trips agrees.
Why would an investing firm ask a puzzle like this?
Because choosing the quantity that stays simple is most of the skill. Here time is simple and distance is messy, so solving in time turns an infinite sum into one multiplication. The same habit finds total cash generated over a period from an average rate instead of adding every quarter, or total interest paid on a loan from the average balance. Say the frame you chose before you give the number.
Where candidates lose it
Candidates start adding the legs, get the first round trip, and then run out of time or nerve at the second. The interviewer is watching whether you step back and find the frame where the problem is one line.
The other loss is saying the distance is infinite because the bird turns infinitely often. Infinitely many legs can have a finite total when each is a fixed fraction of the last; say that, then give 200.
What the interviewer asks next
How many times does the bird turn round before the car arrives?
Where is the car when the bird finishes its second round trip?
If the bird flew at 150 miles an hour, how far would it go?
Asked at BlackRock, Quantitative Research, New York, 2025 (Wall Street Oasis): A car starts at point A going 50 miles an hour towards point B, and a bird starts at point B
074A stock trades at Rs 400 and its EPS is Rs 20. What are its P/E and its earnings yield, and where does the price go if EPS rises 25% and the P/E stays the same?Valuation riddlesWarm upSell-side equity researchIndian brokerage research
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EPS rises 25% and the P/E holds at 20x. Where is the price?
Show the worked solution
A P/E of 20x, an earnings yield of 5%, and a price of Rs 500. P/E is price over EPS, 400 / 20 = 20. The earnings yield is the inverse, EPS over price, 20 / 400 = 5%. If EPS rises 25% to Rs 25 and the market still pays 20 times, the price is 20 x 25 = Rs 500, also 25% higher: at a constant multiple, price moves one for one with earnings.
What does a P/E of 20 actually say?
Buy a small shop for Rs 20 lakh that earns Rs 1 lakh a year and you have paid twenty years of today's profit, a 5% return on your price before any growth. A P/E is the number of years of today's earnings you pay for, and its inverse, the earnings yield, is those earnings as a return on the price. Neither says whether the stock is cheap; that depends on how fast the earnings grow and how risky they are.
Price is the area of EPS times P/E, so a 25% rise in EPS at a constant 20 times widens the rectangle by a quarter from Rs 400 to Rs 500, while a fall in the P/E to 16x would leave the price at Rs 400.
The relationship
$P = \text{EPS} \times \frac{P}{E} \qquad 25 \times 20 = 500 \qquad \text{EY} = \frac{1}{20} = 5\%$
P share price
EPS earnings per share
P/E the multiple the market pays for each rupee of earnings
EY earnings yield, EPS over price
What it says in wordsThe price is earnings per share times the multiple, and the earnings yield is one over the multiple.
When does the price not follow earnings?
When the multiple moves. If EPS rises 25% but the P/E falls from 20x to 16x, the price does not move at all: 25 x 16 = Rs 400. The price change is the earnings change and the multiple change compounded: 1.25 x 0.8 = 1.0. That is how a company can grow profit for years while its share price stands still, and why analysts separate earnings growth from rerating when they explain a move.
Why is the earnings yield worth quoting?
It puts the price on the same scale as other returns. A 5% earnings yield can be set beside a deposit rate or a bond yield, as long as you say what differs: earnings are not all paid out, they can grow, and they are not promised. When bond yields rise above a stock's earnings yield, the case for the stock rests more heavily on growth, which is one reason multiples tend to fall when rates rise.
Where candidates lose it
The slip is adding instead of multiplying: taking the extra Rs 5 of EPS, or 25 rupees, onto the Rs 400 price. The market pays twenty rupees for each rupee of earnings, so Rs 5 more of earnings is Rs 100 more of price.
The quieter loss is saying the earnings yield is a return you receive. It is earnings on price, most of which the company keeps; say that once and the interviewer knows you understand the number.
What the interviewer asks next
EPS rises 25% and the price rises only 10%. What is the new P/E? (17.6x)
What P/E corresponds to an earnings yield of 8%?
Why might two companies with the same EPS growth trade on very different P/Es?
075A company writes Rs 20 crore of inventory down to zero. The tax rate is 25% and the write-down is deductible for tax this year. What happens on each of the three statements?Three statement riddlesWarm upSell-side equity researchIndian brokerage research
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What happens to cash, counting the tax saving?
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Net income falls Rs 15 crore and cash rises Rs 5 crore; inventory falls Rs 20 crore while equity falls Rs 15 crore. The write-down is a Rs 20 crore expense, cut to Rs 15 crore after the Rs 5 crore tax saving. It costs no cash today, so the cash flow statement adds the Rs 20 crore back, leaving cash up by the tax saved. Assets fall Rs 15 crore, and so does equity.
Why does a Rs 20 crore loss raise cash?
A shopkeeper who bought stock last year and finds this year that it has spoiled is not paying for it again; the money went out when the goods came in. Admitting the loss costs nothing new, and if the tax rules let her deduct it, she pays less tax this year. The cash for inventory leaves when it is bought; the write-down only records the loss, and the tax deduction is the one real cash effect today. So profit falls by the loss after tax, while cash rises by the tax saved.
The Rs 20 crore write-down cuts net income by Rs 15 crore after tax, the cash flow statement adds the non-cash Rs 20 crore back to leave cash up Rs 5 crore, and the balance sheet balances with assets and equity both down Rs 15 crore.
How do you walk it through the statements in order?
Income statement first: a Rs 20 crore expense, usually inside cost of goods sold, lowers pre-tax profit by 20; tax falls by 25% of that, Rs 5 crore; net income falls Rs 15 crore. Cash flow statement next: start from net income of minus 15 and add back the Rs 20 crore, because no cash left; cash is up Rs 5 crore. Balance sheet last: cash up 5 and inventory down 20 take assets down 15, and retained earnings fall by the same 15, so the two sides move together.
What if the tax rules are different?
Tax treatment of write-downs varies by jurisdiction, and some rules allow the deduction only when goods are actually scrapped or sold, so confirm it for the case at hand. If the deduction comes later, book net income still falls Rs 15 crore, but cash tax does not change this year, so cash is flat and a Rs 5 crore deferred tax asset appears on the balance sheet instead. Saying this without being asked shows you know where the Rs 5 crore of cash came from.
What does an analyst read into a write-down?
Two things. The charge is usually treated as one-off, so analysts look at profit before it, but repeated write-downs say something about how the company buys and forecasts demand. A write-down also moves cost out of future periods: goods written off now cannot be expensed again when sold, so next year's gross margin can look better than the business really is.
Where candidates lose it
The common slip is saying cash falls by Rs 20 crore, as if the write-down were a payment. The money left when the goods were bought; today's write-down only admits the loss.
The second slip is forgetting tax, which leaves net income down 20 and cash unchanged. With a deductible loss the tax saving is the only cash that moves, and it moves the other way: up Rs 5 crore.
What the interviewer asks next
What changes if the write-down is not deductible for tax until the goods are scrapped?
Next year the written-off goods are sold for Rs 4 crore. What happens on the statements?
Why might a new management team write down inventory heavily in its first year?
088Two stock pitches. Pitch A returns 5x your money with a 10% probability and zero otherwise. Pitch B returns 1.5x with a 60% probability and 0.5x otherwise. Which has the higher expected multiple?Expected value and decisionsWarm upBuy-side equity researchLong-only asset management
Try it first
Which pitch has the higher expected multiple of your money?
Show the worked solution
Pitch B, at 1.1x against 0.5x for Pitch A. Weight each outcome by its probability. A gives 10% of 5x plus 90% of nothing, which is 0.5x: on average it loses half the money. B gives 60% of 1.5x plus 40% of 0.5x, which is 0.9 plus 0.2, 1.1x. A would need better than a one in five chance of the 5x just to break even.
Why does the big number not win?
A lottery ticket that costs Rs 100 and pays Rs 500 one time in ten is a bad ticket, however good Rs 500 sounds. An expected value multiplies each outcome by its probability, so a large payoff is shrunk by a small chance before it counts. For A, 5x shrinks to 0.5x. For B, a modest win that happens more often than not, plus a partial loss that still returns half the money, adds up to 1.1x.
Pitch A's 5x outcome has only a 10% chance and the other 90% returns nothing, so it expects 0.5x, while Pitch B's 60% chance of 1.5x and 40% chance of 0.5x expect 1.1x, above the line where you get your money back.
The relationship
$E[A] = 0.1 \times 5 + 0.9 \times 0 = 0.5\times \qquad E[B] = 0.6 \times 1.5 + 0.4 \times 0.5 = 1.1\times$
E[A], E[B] the expected multiple of money for each pitch
0.1, 0.9, 0.6, 0.4 the probabilities of each outcome
5, 0, 1.5, 0.5 the multiples of money in each outcome
What it says in wordsWeight every outcome by its probability and add: that is what you get on average per rupee put in.
What would make Pitch A worth taking?
Work backwards from breakeven. A returns your money on average only if the chance of the 5x is one in five, 20%. So the real question about A is not how big the upside is but whether you can defend a probability above 20%, double what the pitch claims. That is how a buy-side analyst would push back on a story built around one dramatic outcome: ask for the odds, then check them.
Is the higher expected value the whole answer?
No, and saying so earns the extra point. B still loses half the money 40% of the time, so the expected value tells you which pitch to prefer, not how much to put in. Position size depends on how bad the bad outcome is and how often it comes. The limitation of the question is that it hands you the probabilities. In practice those are the hardest number to estimate, and a pitch with a vivid upside tends to come with an optimistic probability attached.
Where candidates lose it
Candidates are pulled to A by the 5x and justify it with language about asymmetric upside. The interviewer is checking whether you multiply by the probability before you get excited.
The second loss is stopping at the expected value. Mention that B still halves your money 40% of the time, so the choice of pitch and the size of the position are separate questions.
What the interviewer asks next
What probability of the 5x makes A as attractive as B?
If you could hold both, each with half your money, what is the expected multiple and the chance of losing money?
Why might a fund still take a small position in something like Pitch A?
094A company is funded 70% by equity costing 14% and 30% by debt costing 9% before tax. The tax rate is 25%. What is its weighted average cost of capital?Cost of capital and ratesWarm upSell-side equity researchIndian brokerage research
Try it first
Pick the WACC.
Show the worked solution
About 11.8%. Weight each source of money by its share and use debt after tax. Equity contributes 70% of 14%, 9.8 points. Debt costs 9% before tax but only 9% times 75%, 6.75%, after it, so it contributes 30% of 6.75%, about 2.0 points. The total is 11.825%. Using debt before tax would overstate WACC at 12.5%.
Why is WACC a weighted average rather than a simple one?
A household that pays for a flat with 70% of its own savings and a 30% home loan has a blended cost of money closer to what its savings could have earned than to the loan rate, because most of the money is savings. WACC weights each source by its share of the funding, measured at market value, because that is the mix the company's investments must pay for. A simple average of 14% and 9% would give debt far more say than 30% of the money deserves.
Why does the tax rate touch only the debt?
Interest is deducted before tax is worked out; dividends are not. So every Rs 100 of interest cuts the tax bill by Rs 25, and debt at 9% really costs the company 9% times 75%, which is 6.75%. The tax shieldThe reduction in tax a company gets because interest is deductible: interest times the tax rate. is why WACC uses the after-tax cost of debt, and why the equity cost stays as it is. Confirm the applicable tax rate for the company before using a headline figure.
Equity at 70% of funding and a 14% cost contributes 9.8 points and debt at 30% and an after-tax cost of 6.75% contributes 2.025, so WACC is about 11.8%, while using debt before tax would wrongly give 12.5%.
The relationship
$WACC = w_E k_E + w_D k_D (1 - t) = 0.7 \times 14\% + 0.3 \times 9\% \times 0.75 \approx 11.8\%$
w_E, w_D shares of equity and debt in the funding, at market value
k_E, k_D cost of equity and pre-tax cost of debt
t the tax rate, 25%
What it says in wordsWeight each source's cost by its share of the money, and cut the cost of debt by the tax it saves.
What would make you distrust this number?
The weights and the inputs both move. Weights should be market values, not book values, and they should reflect the mix the company will hold over the forecast, not a single year-end snapshot. Adding debt does not lower WACC forever: as borrowing rises, lenders charge more and shareholders demand more for the extra risk. And the tax shield only exists if the company has profits to shield. A loss-making company's debt costs the full 9%, which would lift WACC to 12.5%.
Where candidates lose it
The fast wrong answer is 12.5%, using debt before tax. Candidates remember the formula but drop the one term that makes debt cheaper.
The second loss is applying the tax rate to equity as well, or using book weights without saying so. State market weights and after-tax debt in the first sentence and the interviewer moves on.
What the interviewer asks next
What happens to WACC if the company moves to 50% debt and the cost of equity rises to 16%?
Why should you use market weights rather than book weights?
How does WACC change for a company that pays no tax because of past losses?
097Give a formula for the number of coloured stickers on an n by n by n Rubik's cube, and for the number of small cubes that show on the surface.Probability and brainteasersWarm upT. Rowe PriceBaltimore · 2020
Try it first
For a standard 3 by 3 by 3 cube, how many small cubes show on the surface?
Show the worked solution
Stickers: 6n squared. Cubes on the surface: n cubed minus (n minus 2) cubed. Each of the six faces is an n by n grid of stickers, so there are 6n squared, which is 54 for n of 3. For the cubes, count the hidden core: peeling one layer off every side leaves (n minus 2) cubed, so 27 less 1 is 26 on show. Both formulas need n to be at least 2.
Why are stickers and surface cubes different counts?
A corner cube carries three stickers, an edge cube two and a face-centre cube one. The sticker count measures surface area, while the cube count measures how many pieces touch the surface, and the corners and edges make the first larger than the second. The surface area the question asks for is the sticker count: six faces, each n by n, so 6n squared unit squares.
What is the fast way to count the cubes on show?
Picture a box of laddoos packed three by three by three: to find how many touch the box, count the ones that do not. Only a core with one layer peeled from every side is hidden, so the hidden cubes form an (n minus 2) by (n minus 2) by (n minus 2) block, and everything else shows. For n of 3 that core is a single cube, so 26 show. The subtraction is quicker and harder to get wrong than adding corners, edges and faces.
A 3 by 3 by 3 cube has 27 small cubes and only the single centre cube is hidden, so 26 show on the surface, while six faces of nine stickers carry 54 stickers, and the table gives the same counts for larger cubes.
The relationship
$S(n) = 6n^2 \qquad C(n) = n^3 - (n-2)^3 = 6n^2 - 12n + 8$
S(n) stickers, the surface area in unit squares
C(n) small cubes with at least one face on the surface
n small cubes along one edge, 2 or more
What it says in wordsStickers are six square faces; surface cubes are the whole block less the hidden core, which expands to 6n squared less the overlap at edges and corners.
How do you check the formula before you commit?
Test the smallest case you can picture. A 2 by 2 by 2 cube has no hidden centre, so all 8 pieces show, and the formula gives 8 minus 0, which is 8. Then look at the expanded form: 6n squared counts every face-cube once per face, minus 12n plus 8 removes the double and triple counts along the 12 edges and at the 8 corners. The formula breaks for n of 1, where it gives 2 for a single cube, so state that it holds from n of 2 upwards.
Where candidates lose it
Candidates confuse stickers with cubes and answer 54 cubes, or count six faces of n squared cubes and forget that edge and corner cubes sit on more than one face. Both come from starting at the surface.
The second loss is giving a formula without testing it. Plugging in n of 2 and n of 3 takes ten seconds and catches most slips, and noting that n of 1 fails shows care.
What the interviewer asks next
How many small cubes show exactly two stickers on an n by n by n cube?
For what n are more than half the small cubes hidden?
How would the counts change if the cube were hollow?
Asked at T. Rowe Price, Equities, Baltimore, 2020 (Wall Street Oasis): Give an equation that yields the surface area of an n by n by n Rubic's cube based on number of blocks per side.
098Estimate how many cups of tea are sold in a day at a busy railway station.Market sizing and estimationWarm upConsulting style estimationResearch KPO and GCC
Try it first
Where should the estimate start?
Show the worked solution
About 1.5 lakh cups a day on these assumptions. Take 5 lakh passengers. The 2 lakh long-distance travellers wait long enough that one in two buys a cup: 1 lakh cups. The 3 lakh commuters rush through, one in ten buys: 30,000. Staff, porters and drivers, say 5,000 people at three cups, add 15,000. That gives 1,45,000, and 50 stalls selling about 3,000 cups each agrees.
Why start from people and not from stalls?
If you wanted to know how many samosas a school canteen sells, you would count students and ask how many buy one at break, not count the frying pans. Demand comes from the people passing through, so the estimate starts with footfall and a buying rate; the stall count is useful only as a check on capacity. Starting from stalls forces you to guess sales per stall, which is the very number you are trying to find.
State every number as an assumption. Assume a busy junction handles about 5 lakh passengers a day. Split them by how long they stay: long-distance travellers wait on the platform for trains that may be late, while suburban commuters walk straight through. The split matters because waiting time drives tea buying far more than the station's size does. Give long-distance travellers a rate of one cup for every two people and commuters one in ten.
Passenger flow peaks in the morning and evening, and applying buying rates to 2 lakh long-distance travellers and 3 lakh commuters gives about 1,30,000 cups, to which station staff add 15,000, about 1,45,000 cups a day.
How do you check it from the supply side?
Count the sellers. Suppose a big station has about 50 stalls and trolleys. A busy stall can pour a cup every 20 seconds for much of a 17-hour day, about 3,000 cups. 50 sellers at 3,000 cups is 1,50,000, close to the 1,45,000 from the demand side, so the two routes agree. If they had disagreed by a factor of three, you would know one buying rate or the footfall figure was off and could say which one you distrust.
What would you refine with more time?
The long-distance buying rate carries most of the answer, so refine it first. Waiting time varies with delays, time of day and weather: a winter morning sells far more tea than a summer afternoon. A sharper estimate would split the day into blocks and apply a rate to each, which is what the hourly chart does. The limitation is that footfall itself is an assumption here; railway data on passengers per day for the specific station would replace it.
Where candidates lose it
Candidates start from stalls, guess a sales figure per stall and multiply, which makes the answer a single unchecked guess. Others multiply every passenger by one cup, ignoring that a commuter running for a local train rarely stops.
The second loss is giving a number with no cross-check. The supply-side count takes twenty seconds and turns an estimate into a reasoned range.
What the interviewer asks next
How would the answer change on a foggy winter day with long delays?
What would the annual tea revenue of the station be?
How would you estimate the number of stalls the station can support?
100A company starts its April to March financial year with 100 crore shares and issues 20 crore new shares on 1 October. Net income for the year is Rs 330 crore. What is EPS?EPS and share countWarm upIndian brokerage researchResearch KPO and GCC
Try it first
Which share count goes under the Rs 330 crore?
Show the worked solution
Rs 3.00, on 110 crore weighted average shares. The 100 crore opening shares count for the full year. The 20 crore new shares existed only from 1 October, half the year, so they count as 10 crore. Rs 330 crore over 110 crore is Rs 3.00. Dividing by the year-end 120 crore would understate EPS at Rs 2.75.
Why weight the shares by time?
A flat shared by two people for six months and three people for the next six has housed two and a half people on average over the year, and splitting the annual electricity bill by three would overcharge the one who arrived late. EPS divides a full year's profit by the shares that were outstanding while it was earned, so shares issued mid-year count only for the part of the year they existed. The money raised on 1 October only helped earn profit in the second half.
The company had 100 crore shares from April to September and 120 crore from October to March, a time-weighted average of 110 crore, so Rs 330 crore of net income gives EPS of Rs 3.00.
The relationship
$\bar N = 100 + 20 \times \frac{6}{12} = 110 \qquad EPS = \frac{330}{110} = 3.00$
N bar the weighted average number of shares, crore
6/12 the share of the year the new shares were outstanding
330 net income for the year, Rs crore
What it says in wordsCount each share for the fraction of the year it existed, then divide the year's profit by that average.
When is the time weighting not used?
When no new money comes in. A bonus issue or a share split changes the number of shares without changing the company's resources, so it is applied to the whole year and to comparative years as if it had always happened. If the 20 crore shares had been a bonus issue, the count would be 120 crore for the full year and EPS Rs 2.75, with last year's EPS restated on the same basis. Confirm the exact treatment against the current accounting standard on earnings per share, Ind AS 33 in India.
Why does an analyst care about the difference?
Because next year's EPS starts from 120 crore shares for the full twelve months. If profit stays at Rs 330 crore, EPS falls to Rs 2.75 next year even though nothing got worse, simply because the new shares count for a full year. An analyst forecasting growth in EPS has to model the share count forward, not just the profit, or the forecast will look better than the business.
Where candidates lose it
The common slips are dividing by the closing 120 crore, which gives Rs 2.75, or by the opening 100 crore, which gives Rs 3.30. Both ignore when the shares were issued.
The follow-up catches the rest: candidates who time-weight a bonus issue as if it were a fresh issue for cash have missed the one case where the rule changes.
What the interviewer asks next
The 20 crore shares were a bonus issue instead. What is EPS?
If the issue had been on 1 January, what would the weighted count be?
What will EPS be next year if net income stays at Rs 330 crore?

t_2x	years to double
t_8x	years to grow eightfold
72	the rule of 72 constant
12	the growth rate in percent

Rate	Rule of 72	Exact doubling time
4%	18.0 years	17.67 years
8%	9.0 years	9.01 years
12%	6.0 years	6.12 years
18%	4.0 years	4.19 years
24%	3.0 years	3.22 years

3 / (3 x 3)	reports per analyst-day, one third
9 x 9	analyst-days in the new case, 81

v_bird	the bird's speed, 100 miles an hour
t_car	the car's travel time, 2 hours
133.3	the bird's first round trip in miles
1/3	the ratio of each round trip to the one before

Try it first

Why does 72 divided by the rate work?

Why is eightfold 18 years and not 48?

Where does an analyst use this?

Where candidates lose it

What the interviewer asks next

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Why does the fast answer of 9 feel right?

How do you do it in ten seconds?

What is a timed test like this really checking?

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What is the shortcut, and why does it work?

How do you check it the long way?

Why would an investing firm ask a puzzle like this?

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What does a P/E of 20 actually say?

When does the price not follow earnings?

Why is the earnings yield worth quoting?

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What the interviewer asks next

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Why does a Rs 20 crore loss raise cash?

How do you walk it through the statements in order?

What if the tax rules are different?

What does an analyst read into a write-down?

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Why does the big number not win?

What would make Pitch A worth taking?

Is the higher expected value the whole answer?

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Why is WACC a weighted average rather than a simple one?

Why does the tax rate touch only the debt?

What would make you distrust this number?

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Why are stickers and surface cubes different counts?

What is the fast way to count the cubes on show?

How do you check the formula before you commit?

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Why start from people and not from stalls?

How do you check it from the supply side?

What would you refine with more time?

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What the interviewer asks next

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Why weight the shares by time?

When is the time weighting not used?

Why does an analyst care about the difference?

Where candidates lose it

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