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 20 more shares than Chetan at the end of days 5, what was the price of the shares at the and of day 3?

  1. 90

  2. 100

  3. 110

  4. 120
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A Correct answer
Explanation

For Michael to end up with 20 more shares than Chetan, we analyze the possible price paths. Chetan always ends up with 10 fewer shares than his starting amount. Thus, Michael must end up with 10 more shares than his starting amount. This is only possible if Michael bought shares when the price went below 90 (i.e., reached 80). The only path satisfying this and ending at 110 on day 5 requires the price at the end of day 3 to be 90.

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