The price of commodity X increases by 40 paise every year, while the price of…

2024

The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y?

  1. A.

    2010

  2. B.

    2011

  3. C.

    2056

  4. D.

    2035

Attempted by 7 students.

Show answer & explanation

Correct answer: B

Step-by-Step Solution

To determine the year in which commodity X costs 40 paise more than commodity Y, we can set up an algebraic equation based on the annual price increase.

  1. Establish the initial prices in paise:

    • Initial price of commodity X (in 2001) = Rs. 4.20 = 420 paise.

    • Initial price of commodity Y (in 2001) = Rs. 6.30 = 630 paise.

  2. Define the variables and annual increase:

    • Let 'z' be the number of years after 2001.

    • Annual increase for X = 40 paise/year.

    • Annual increase for Y = 15 paise/year.

    • Price of X after 'z' years = 420 + 40z.

    • Price of Y after 'z' years = 630 + 15z.

  3. Set up the equation for the condition "X costs 40 paise more than Y":

    • (420 + 40z) - (630 + 15z) = 40

    • (420 - 630) + (40z - 15z) = 40

    • -210 + 25z = 40

    • 25z = 40 + 210

    • 25z = 250

    • z = 10 years.

  4. Determine the final year:

    • The year = 2001 + 10 = 2011.

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