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 Chetan ended up with Rs.1300 more cash than Michael at the end of day 5, what was the price of the MCS share at the end of day 4?

  1. Rs. 90

  2. Rs. 100

  3. Rs. 110

  4. Rs. 120
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B Correct answer
Explanation

The price sequence that results in Chetan having exactly Rs.1300 more than Michael is: Day 1 (Rs.90), Day 2 (Rs.80), Day 3 (Rs.90), Day 4 (Rs.100), Day 5 (Rs.110). Chetan's strategy of buying when prices fall and selling when they rise gives him better returns compared to Michael who only trades at extreme prices. At day 4's Rs.100 price, both traders are in a neutral position relative to their strategies, setting up the final difference.

AI explanation

Working through every valid sequence of three up-days and two down-days that starts at Rs.100 and ends at Rs.110, Chetan's fixed trading rule (sell on up days, buy on down days) always nets him exactly Rs.1300 more raw cash than a no-trade baseline, regardless of the path. Michael only trades when a closing price strictly exceeds Rs.110 or drops below Rs.90; the only paths where Michael never crosses those thresholds (so the gap stays exactly Rs.1300) are the ones where the day-4 closing price is Rs.100. So Rs.100 is the price consistent with the stated Rs.1300 gap.

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