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23 July, 22:31

The value of a two-digit number exceeds twice the sum of its digits by 19. The tens digit is two less than the units digit. Find the number.

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  1. 23 July, 22:39
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    Answer with Step-by-step explanation:

    Let the ones digit of the number be y

    and tens digit of the number be x.

    The tens digit is two less than the units digit.

    i. e. x=y-2

    The value of the number exceeds twice the sum of its digits by 19.

    i. e. 10x+y=2 (x+y) + 19

    10 (y-2) + y=2 (y-2+y) + 19

    10y-20+y=2 (2y-2) + 19

    11y-20=4y-4+19

    11y-4y=20-4+19

    7y=35

    dividing both sides by 7, we get

    y=5

    Putting value of y in x=y-2, we get

    x=3

    10x+y=10*3+5

    =35

    Hence, the two digit number is:

    35
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