Date of equal tea prices

CAT 2007 Slot 1 · Quantitative Ability · Medium · Linear Equations

This is a medium Quantitative Ability question from the CAT 2007 Slot 1 paper. It tests Linear Equations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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.

Related Linear Equations questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace