Comprehension

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:

Question: 1

If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

Show Hint

Always track day-by-day price changes when constraints involve multiple consecutive actions.
Updated On: Jul 31, 2025
  • Rs 90
  • Rs 100
  • Rs 110
  • Rs 120
  • Rs 130
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The Correct Option is D

Solution and Explanation

Chetan sells only when the price increases from the previous day. If he sells on three consecutive days, it means the price increased for three straight days.
Starting at Rs 100 on Day 1:
Day 1 end: Rs 110, Day 2 end: Rs 120, Day 3 end: Rs 130.
Michael sells only when the price $>$ Rs 110, and he sells only once in the five days. To satisfy this condition, the only possible price for Day 3 is Rs 120. \[ \boxed{\text{Rs 120}} \]
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Question: 2

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

Show Hint

If several price paths are possible under given constraints, the Correct Answer is “Not uniquely determinable.”
Updated On: Jul 31, 2025
  • Rs 90
  • Rs 100
  • Rs 110
  • Rs 120
  • Not uniquely determinable
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The Correct Option is

Solution and Explanation

The Rs 1300 cash difference could result from multiple valid trading sequences that meet all constraints. Different sequences can lead to different Day 4 prices. Hence, the answer cannot be determined uniquely. \[ \boxed{\text{Not uniquely determinable}} \]
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Question: 3

If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of MCS share at the end of day 3?

Show Hint

Share differences at the end are tied directly to buy/sell triggers over the days.
Updated On: Jul 31, 2025
  • Rs 90
  • Rs 100
  • Rs 110
  • Rs 120
  • Rs 130
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The Correct Option is B

Solution and Explanation

Michael buys when the price $<$ Rs 90 and sells when the price $>$ Rs 110. Chetan’s trades occur in the opposite market moves. Ending up with 20 more shares means Michael accumulated more shares when prices were low. The only price pattern that matches this share difference gives Day 3 price = Rs 100. \[ \boxed{\text{Rs 100}} \]
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Question: 4

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?

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If the number of shares is the same, differences in wealth come only from cash differences.
Updated On: Jul 31, 2025
  • Michael had 10 less shares than Chetan.
  • Michael had 10 more shares than Chetan.
  • Chetan had 10 more shares than Michael.
  • Chetan had 20 more shares than Michael.
  • Both had the same number of shares.
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The Correct Option is

Solution and Explanation

A cash difference without a difference in share holdings means both ended with the same number of shares but different total cash. \[ \boxed{\text{Both had the same number of shares}} \]
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Question: 5

What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

Show Hint

To maximise profit, align buying at absolute lows and selling at absolute highs, respecting all trading rules.
Updated On: Jul 31, 2025
  • Rs 3700
  • Rs 4000
  • Rs 4700
  • Rs 5000
  • Rs 6000
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The Correct Option is D

Solution and Explanation

Maximising cash means both traders sold at the highest possible prices and bought at the lowest possible prices within the constraints. The maximum difference achievable through optimal trades is Rs 5000. \[ \boxed{\text{Rs 5000}} \]
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