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Rajan@2021
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If 2 is added to each one of the two given number,then their ratio becomes 1:2 However if 4 is subtracted from each of the given number,the ratio becomes 5:11.Find the number.

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One of the most important and conceptual question from linear equations in two variables in which we have to find the numbers if 2 is added to each one of the two given number,then their ratio becomes 1:2 However  if 4 is subtracted from each of the given number,the ratio becomes 5:11.

RS Aggarwal, Class 10, Chapter 3E, question no 9

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  1. Let the required numbers be x and y.

    Now, we have:  x+2/ y+2 = 1/2

    By cross multiplication, we get:

    2x + 4 = y + 2

    ⇒ 2x – y = -2 ……(i)

    Again, we have:

    x−4/ y−4 = 5/11

    By cross multiplication, we get:

    11x – 44 = 5y – 20

    ⇒11x – 5y = 24 ……(ii)

    On multiplying (i) by 5,

    we get:

    10x – 5y = -10

    On subtracting (iii) from (ii),

    we get:

    x = (24 + 10) = 34

    On substituting x = 34 in (i),

    we get:  2 × 34 – y = -2

    ⇒ 68 – y = -2

    ⇒ y = (68 + 2) = 70

    Hence, the required numbers are 34 and 70.

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