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.

Question 39

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


The above table includes the values of the share price at the end of each day. Chetan and Michael column shows the number of shares at the end of 5th day with Chetan and Michael respectively. (-10 means he has sold 10 shares, +10 means he has bought 10 shares)

there are 10 different possible cases according to the initial and final share price.

Please note that Chetan will always be having -10 shares(10 shares sold) and 1300 as cash.

This is because Chetan buys for every fall in price and sells for every rise in price. But the fluctuation in share price is constant as it starts from 100 and closes at 110 on day 5. So, in total Chetan will always sell 10 shares in all 5 days combined.

As Chetan has sold 10 shares, he'll get 110*10 =1100 cash because of it in every case. Also, Chetan earns Rs. 200 in every case because of buying at low and selling at high. So total cash Chetan will always have after 5 days = 1100+200 =1300.

The question asks about the case where there has been the maximum possible increase in the combined cash balance of Chetan and Michael at the end of the fifth day.

As we know chetan has 1300 cash in all the cases , so we have to maximize the case where Michael has the most cash.

Also, if we see clearly, the profit made by selling and buying is in hundreds while the cash received by selling the shares is much far in terms of cash.
As 10 shares sold give = 10*110 = 1100 cash. So we have to look at the case where Michael has sold most shares which is case 8.

In case 8 the price rises from 100 to 110 ->120 ->130 ->120 ->110

in this case 110(0 new shares)->120(Michael sold 10 shares)->130(Michael sold 10 shares)120(Michael sold 10 shares)->110(Michael does nothing) = 30 shares sold in total

Cash =  20 shares at 120 and 10 shares at 130 =  120*20+130*10 = 2400+1300 =3700

As Chetan has 1300 cash and Michael has 3700 cash;
total cash they have is : 3700+1300 =5000

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