Question

the digit of a two digit number differ by 3 if the digits interchange and the resulting number is added to the original number we get 143 what can be the original number

Answer 1

Solution -

Let the digit in ones place be x

So, the digit in tens place be x + 3

Original no. = 10(x + 3) + 1(x)

= 10x + 30 + x

= 11x + 30

New no. = 10(x) + 1(x + 3)

= 10x + x + 3

= 11x + 3            [By reversing the digits]

According to Question,

Original no. + New no. = 143

(11x + 30) + (11x + 3) = 143

⇒ 22x + 33 = 143      [By transposition]

⇒ 22x = 143 - 33

⇒ 22x = 110               [By transposition]

⇒ x = 110 / 22

⇒ x = 5

Required Numbers -

Original no. = 11x + 30 = 11(5) + 30

= 55 + 30

= 85

New no. = 58   [By reversing the digits]

Hence, the required number is either 85 or 58

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Answer 2

Answer:

Let the digits of the number be = x, y

We get to know that :

x - y = 3 ( when 'x' > 'y' ) ...(1)

Now, original number = 10x + y

Now, original number = 10x + yDigits reversed, we get = 10y + x

According to the question now :

10x + y + 10y + x = 143

=》 x + y = 13 ...(2)

Eliminate "y" from both the equations... you get :

x = 8

x = 8y = 5

Original Number = 85