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Rajan@2021
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The difference between two numbers is 14 and the difference between their squares is 448 . Find the numbers.

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An important and exam oriented question from linear equations in two variables in which we have to find the numbers if difference between two numbers is 14 and the difference between their squares is 448

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

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  1. Let us consider,
    First number =x and
    Second number =y
    (Assume y is smaller)
    As per the statement,
    xy=14....(1)
    and =448
    (x+y)(xy)=488
    (x+y)×14=448
    x+y=32....(2)
    Adding (1) from (2)
    2x=46 or x=23
    Subtracting (1) from (2)
    2y=18 or y=9
    Answer
    Numbers are 23 and 9

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