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

2023

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.

    2020

  2. B.

    2011

  3. C.

    2098

  4. D.

    2145

Attempted by 2 students.

Show answer & explanation

Correct answer: B

Step-by-Step Solution

To find the year in which the price of commodity X will be 40 paise more than commodity Y, we can set up an equation based on the number of years passed.

  1. Define the variables:

    • Let n be the number of years after 2001.

    • Commodity X price in 2001 = Rs. 4.20 = 420 paise.

    • Commodity Y price in 2001 = Rs. 6.30 = 630 paise.

    • Annual increase for X = 40 paise.

    • Annual increase for Y = 15 paise.

  2. Set up the equation for the price after n years:

    • Price of X after n years = 420 + 40n

    • Price of Y after n years = 630 + 15n

  3. Apply the condition (X = Y + 40):

    • (420 + 40n) = (630 + 15n) + 40

    • 420 + 40n = 670 + 15n

    • 40n - 15n = 670 - 420

    • 25n = 250

    • n = 10

  4. Determine the year:

    • The year = 2001 + 10 = 2011.

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