One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and

Question

One of the two digits of a two digit number is three times the other digit. If you
interchange the digits of this two-digit number and add the resulting number to the
original number, you get 88. What is the original number?​

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Julia 5 days 2021-10-08T21:15:07+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-08T21:16:26+00:00

    Question

    One of the two digits of a two digit number is three times the other digit. If you

    interchange the digits of this two-digit number and add the resulting number to the

    original number, you get 88. What is the original number?

    \rule{230}2

    • let the digit be at tens place x and unit place be y

    Given

    • one of the two digit number is 3 times of the other digit .

    → y = 3

    Therefore

    Original two digit number is = 10x + 3x

    After interchanging the digit

    \sf→ 10×3x+x\\\sf→ 30x+x\\\sf→ 31x

    Given,

    • After adding the resulting number to the original number , we get 88

    \sf→ 10x+3x+31x=88\\\sf→ 13x+31x=88\\\sf→ 44x=88\\\sf→ x=\frac{88}{44}\\\sf→ x= 2

    Hence,

    the digit at tens place is 2

    Now,

    The digit at unit place is = 3(2) = 6

    Therefore

    The original number is 26.

    0
    2021-10-08T21:16:32+00:00

    The answer to the question is ‘26′ or ‘62′.

    Let a digit be x (no matter units place or tens digit place) the the other digit will be 3x. Since 3x has to be a single-digit non-zero no. so x can only be either 1,2 or 3.

    So the no. is (let it be ‘a’) a= x _3x (Now assuming x to be tens digit..You can also take it as units digit).

    Then according to the question:

    interchanged no. (let it be ‘b’) b= 3x_x.

    now,

    a+b=88 ……..(Given)

    Since x can only be 1,2 or 3.

    so addition would take no carry on.

    so a+b=4x_4x=88.

    comparing both places:

    4x=8

    and 4x=8.

    (both equations are same)

    so x=2.

    So no. is either 26 or 62.

    You can also see a=10*x+3x=13x

    (As a 2-digit no. is of the form 10a+b,where both a,b are single digit no.s ‘a’ not equal to 0. )

    similarly b=10*3x+x=31x

    a+b=44x=88.

    x=2.

    so a=26 (or 62 according to what you have taken as tens digit.)

    THANK YOU.

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