CAT 2006 — DILR Question 15
Answer the following question based on 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.
If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?
Answer & solution
Rs. 90
- B
Rs. 100
- C
Rs. 110
- D
Rs. 120
- E
Rs. 130
Let the price of the share rise on x days and fall on y days. As the price increases by Rs. 10 in the five days, we have:
x + y = 5 and 10x – 10y = 10
Solving the above two equations simultaneously, we have
x = 3 and y = 2
The price of the share goes up on 3 days and falls on 2 days.
The three days on which the price rises can be selected in 5C3 = 10 ways
The following are the 10 cases:
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Consider Case 5:
Chetan sells on Days 1, 2 and 4 and buys on days 3 and 5.
Change in the number of shares he has = –30 + 20 = –10
Change in his cash = 10 × (110 + 120 + 120) – 10 × (110 + 110) = Rs. 1300
Michael sells on days 2 and 4, but never buys as the share price does not go below Rs. 90.
Change in the number of shares he has = –20
Change in his cash = 10 × (120 + 120) = Rs. 2400
The other cases are evaluated in a similar manner and the data is tabulated as shown above.
Chetan sold on three consecutive days: Cases 1, 2 and 3.
Michael sold only once: Case 3.
This information corresponds to case 2 from the table. The price at the end of day 3 was Rs. 90.
Hence, option (a).