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Rajan@2021
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Find a fraction which becomes ( 1/2 ) when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes ( 1/3 ) when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

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An important and exam oriented question from linear equations in two variables as it was already asked in various examinations in which we have given that when 1 is subtracted from the numerator, the fraction becomes 1/2 and when 2 is added to the denominator, and the fraction becomes ( 1/3 ) when 7 is subtracted from the numerator and 2 is subtracted from the denominator. And we asked to find the fraction

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 22

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1 Answer

  1. Let the required fraction be x/y .  Then, we have:

    x−1/ y+2 = 1/2

    ⇒ 2(x – 1) = 1(y + 2)

    ⇒2x – 2 = y + 2

    ⇒2x – y = 4 ……(i)

    Again, x−7/ y−2 = 1/3

    ⇒3(x – 7) = 1(y – 2)

    ⇒3x – 21 = y – 2

    ⇒ 3x –y = 19 ……(ii)

    On subtracting (i) from (ii), we get:  x = (19 – 4) = 15

    On substituting x = 15 in (i), we get:  2 × 15 – y = 4

    ⇒ 30 – y = 4

    ⇒y = 26

    ∴ x = 15 and y = 26

    Hence, the required fraction is 15/26

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