Multiple choice general knowledge math & puzzles

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 on 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)?

  1. Michael had 10 less shares than Chetan.

  2. Michael had 10 more shares than Chetan.

  3. Chetan had 10 more shares than Michael.

  4. Both had the same number of shares.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let $U$ be the number of days the price went up and $D$ be the number of days it went down. Since the price went from 100 to 110 over 5 days with steps of $\pm 10$, we have $U + D = 5$ and $10(U - D) = 10$, which yields $U = 3$ and $D = 2$. Chetan sells 10 shares on up days and buys 10 on down days, ending with $30 - 20 = 10$ fewer shares. Michael only trades if the price goes above 110 or below 90. Analyzing the valid price paths shows that Michael's cash difference of -100 relative to Chetan forces both to end up with the same number of shares.

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