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Question:

The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the n^th 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 n^th day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?

Explanation:

Note that the price of Darjeeling tea remains constant after the 100^th 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 20^th May.

Hence, option (c).