CAT 2007 — QA Question 1
The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?
Answer & solution
- A
May 21
- B
April 11
May 20
- D
April 10
- E
June 30
Note that the price of Darjeeling tea remains constant after the 100th day (n = 100).
If the prices of the two varieties of tea become equal before n = 100, then
100 + 0.1n = 89 + 0.15n
∴ n = 220, which is not possible. (since n is assumed to be less than 100)
∴ The prices of the two varieties will be equal after n = 100,
i.e., when the price of Darjeeling tea = 100 + 0.1 × 100 = 110
∴ 89 + 0.15n = 110
∴ n = 140
2007 is not a leap year. Number of days till 30th April = 31 + 28 + 31 + 30 = 120
The prices of the two varieties will be equal on 20th May.
Hence, option (c).