Date of equal tea prices

CAT 2007 Slot 1 · QA · Medium · Linear Equations

The price of Darjeeling tea (in rupees per kilogram) is 100+0.10n100 + 0.10n, on the nthn^{\text{th}} day of 2007 (n=1,2,,100n = 1, 2, \dots, 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89+0.15n89 + 0.15n, on the nthn^{\text{th}} day of 2007 (n=1,2,,365n = 1, 2, \dots, 365). On which date in 2007 will the prices of these two varieties of tea be equal?

  1. A.

    May 21

  2. B.

    April 11

  3. C.

    May 20

  4. D.

    April 10

  5. E.

    June 30

Answer

C

Explanation

On n=100n = 100, Darjeeling tea price =100+10=110= 100 + 10 = 110. For Ooty tea price to reach 110: 89+0.15n=110    0.15n=21    n=14089 + 0.15n = 110 \implies 0.15n = 21 \implies n = 140. Days in Jan (31) + Feb (28) + Mar (31) + Apr (30) =120= 120. Day 140 is May 20.

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