the digits of two numbers differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143.

Question

the digits of two numbers differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143. What is the original number ​

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Katherine 2 weeks 2021-09-07T07:51:48+00:00 2 Answers 0 views 0

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    0
    2021-09-07T07:52:51+00:00

    Answer:

    \huge\mathcal{Question:}

    The digits of two numbers differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143. What is the original number .

    \huge\mathcal{Answer:}

    Let the two digits be x and y (where x is at tens place and y is at once place)

    so the number we get is 10x+y

    x – y = 3 …..(given in the Question) —–eq1

    Now interchanging the digits , we get

    The new number is 10y+x because now x is at once place and y is at the tens place.

    now,

    old number + new number = 143 (given). —–eq2

    now putting the values,

    10x+y+10y+x = 143

     \implies 11x + 11 y = 143

     \implies 11(x+y) = 143

     \implies x+y = \sf\frac{143}{11}

     \implies x+y = 13

    now from eq1 ,we come to know that y = 3+x

    so putting y = 3x , we get

    x+(x+3) = 13

     \implies 2x+3 = 13

     \implies 2x = 10

     \implies x = 5

    so now from y = x+3 , we get the value of y to be 8.

    So the original number is 10×5 + 8 =58

    \boxed{Answer=58}

    0
    2021-09-07T07:53:08+00:00

    Answer:

    Let the number be xy

    Y= x-3

    Number formed:

    10(x)+ x-3 [x will be multiplied by 10 because of its place]

    10x+(x-3)

    Reversed number= yx

    = 10(x-3)+x [x-3 will be multiplied by 10 because of its place]

    = 10x-30+x

    Sum of the numbers= 143

    10x+(x-3)+10x-30+x= 143

    11x+11x-3-30= 143

    22x-33= 143

    22x= 143+33

    22x= 176

    X= 176/22

    X= 8

    NUMBERS FORMED:

    xy= 58

    Yx= 85

    VERIFY:

    The sum of both the numbers should be equal to 143. Using this statement, we can verify our answer.

    Xy+yx= 143

    58+85= 143

    143= 143

    LHS= RHS

    Hence, verified

    Hope it helps

    Please mark my answer as BRAINLIEST

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