Two traders, Chetan and Michael, were involved in the buying and selling of…
2024
Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs 100, while at the end of the fifth day it was priced at Rs 110. At the end of each day, the MCS share price either went up by Rs 10 or else, it came down by Rs 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days. Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price. If any day, the closing price was above Rs 110, then Michael sold 10 shares of MCS, while if it was below Rs 90, he bought 10 shares, all at the closing price.
If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?
- A.
Both had the same number of shares.
- B.
Michael had 10 less shares than Chetan
- C.
Michael had 10 more shares than Chetan
- D.
Chetan had 10 more shares than Michael
Show answer & explanation
Correct answer: A
Concept: this is a state-tracking puzzle. A scenario evolves day by day under a fixed rule for each actor, and more than one day-by-day path can satisfy the rules alone (any sequence of price ups and downs consistent with the start and end price). A single numeric fact given about the final state (here, the cash gap between the two traders) is what pins down which path(s) actually happened - so the method is to enumerate every rule-consistent path, apply each actor's own trading rule day by day, and keep only the path(s) whose resulting numeric outcome matches the one fact given.
Application: since the price must move Rs 10 net upward over five days of +-Rs 10 moves, exactly 3 of the 5 days must be up-days and 2 must be down-days - there are 10 such orderings in total. Chetan trades on every single day (sells 10 on an up day, buys 10 on a down day), so regardless of which ordering actually occurred, his share count always falls by exactly 10 (3 sales minus 2 buys) - this does not depend on the specific ordering at all. One representative ordering that is consistent with every rule in the question:
Day | Opening Price (Rs) | Closing Price (Rs) |
|---|---|---|
Day 1 | 100 | 110 |
Day 2 | 110 | 120 |
Day 3 | 120 | 110 |
Day 4 | 110 | 100 |
Day 5 | 100 | 110 |
Chetan's rule applies every day; Michael's rule applies only when the closing price is above Rs 110 or below Rs 90:
Day | Closing Price (Rs) | Chetan's action | Michael's action |
|---|---|---|---|
Day 1 | 110 | Sold 10 shares at Rs 110 (price rose) | No trade (Rs 110 is not above Rs 110) |
Day 2 | 120 | Sold 10 shares at Rs 120 (price rose) | Sold 10 shares at Rs 120 (Rs 120 is above Rs 110) |
Day 3 | 110 | Bought 10 shares at Rs 110 (price fell) | No trade |
Day 4 | 100 | Bought 10 shares at Rs 100 (price fell) | No trade |
Day 5 | 110 | Sold 10 shares at Rs 110 (price rose) | No trade |
Chetan's share count changes by -10 -10 +10 +10 -10 = -10 in this ordering, matching the fixed -10 that holds for every one of the 10 orderings.
Chetan's cash changes by +1,100 +1,200 -1,100 -1,000 +1,100 = +Rs 1,300.
Michael trades only on Day 2 in this ordering, so his share count changes by -10 as well - the same size change as Chetan's, from the same starting count - and his cash changes by +Rs 1,200.
Checking all 10 possible day-orderings the same way (not just the one shown above) shows only 3 of them reproduce a cash gap of exactly Rs 100 with Chetan ahead - and in every one of those 3 orderings, Michael's share count also falls by exactly 10, matching Chetan's exactly. So the two end up holding the same number of shares in every ordering consistent with the given Rs 100 fact, not merely in the representative case above.
In this representative ordering the cash gap comes out to Rs 1,300 - Rs 1,200 = Rs 100, exactly matching the figure given in the question, confirming it is one of the 3 valid orderings.
Cross-check: an independent scale check confirms the same conclusion without the full enumeration. Each unit of share-count difference between the two traders is created by one extra completed 10-share trade near the prevailing price (roughly Rs 100 to Rs 120), so a genuine share-count gap should show up as a cash gap of a similar size - on the order of Rs 1,000, not Rs 100. Working through the orderings that DO produce a 10-share gap confirms this directly: they instead produce a cash gap of about Rs 1,100 to Rs 1,300 - an order of magnitude larger than, and in one case the opposite direction from, the Rs 100 the question actually gives. A share-count gap is therefore incompatible with the stated Rs 100 cash gap.
Result: both traders end Day 5 holding the same number of shares - the difference is 0.