Answer the following questions on the basis of the information given below:
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.
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?
(1) Rs.90 (2) Rs.100 (3) Rs.110 (4) Rs.120 (5) Rs.130
2. 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 (5) Not uniquely determinable
3. 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) Rs.90 (2) Rs.100 (3) Rs.110 (4) Rs.120 (5) Rs.130
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)?
(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) Chetan had 20 more shares than Michael.
(5) Both had the same number of shares.
5. What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?
(1) Rs.3700 (2) Rs.4000 (3) Rs.4700 (4) Rs.5000 (5) Rs.6000
Answers:
1.(3)
2.(2)
3.(1)
4.(5)
5.(4)
Explanation:
Here the total increase in the price of the share is Rs.10.
Hence, of the five days, there must be an increase for three of the five days and there is decrease for two days.
1. (3) Given that, Michael sold 10 shares only once. Hence, the price is more than 110 for only one day and on all the remaining days it is not more than 110. We can get the share price as 120 with three increase and two decreases. But as the three increases are on consecutive days, the three days can be (Day 1, Day 2, Day 3) or (Day 2, Day 3, Day 4,) or (Day 3, Day 4, Day 5). But it cannot be (Day 1, Day 2, Day3), the reason being that the price will be more than 110 on day 2 as well as Day 3, It cannot be (Day 3, Day 4, Day 5) the reason being that the price cannot be 120 on any of the days.
The increase must be on (Day 2, Day3, Day4,).
There is a decrease on Day 1 and Day 5
The price at the end of Day 3 is 100-10+10+10=110.
2. (2) Given that Chetan ended up with Rs.1300 more than Michael at the end of Day 5. The maximum possible change in the amount with Chetan with Rs.1300, as he sells shares on three days and buys shares on the remaining two days.
Michael should not have sold any shares and also he should not have bought any shares.
The share price did not cross 110 or did not fall below 90 on any of the days. The price of the share at the end of Day 4 cannot be 120. It must be 100.
3. (1) Chetan will sell 10 shares each for three days and buy shares for two days. Hence, if he had x shares at the beginning of Day 1, he finally had (x-10) shares at the end of Day 5. Michael had (x+10) shares on Day 5. He bought 10 shares on one of the five days i.e shares price should be less than 90 on that day. It should be 80. Hence, the only possibility is 100-90-80-90-100-100 Day 1 Day 2 Day 3 Day 4 Day 5 It is 90 at the end of Day 3.
4. (5) If the difference in the shares is 10 or more, the difference in the amounts would be close to Rs.1000, but it is given the difference is Rs.100.
The number of shares with them must be the same. The following table represents one of the possibilities where Michael ended up with Rs.100 less than Chetan, while both of them ended up with the same number of shares.
Beginning Ending
Day 1 100 110
Day 2 110 120
Day 3 120 110
Day 4 110 100
Day 5 100 110
5.(4) The maximum possible cash balance is possible, when both of them sell the maximum number of shares.
That happens in the following case.
Beginning Ending
Day 1 100 110
Day 2 110 120
Day 3 120 130
Day 4 130 120
Day 5 120 110
The change in amount with Chetan
= (110×10) + (120×10) + (130×10) – (120×10) – (110×10) =1300
That with Michael = (120×10) + (130×10) + (120×10) = 3700
Total = Rs.5000.
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