Question

The digits of a two digit number differ by 3. if the digits are interchanged and the resulting number is added to the original number, we get 143, find the original number. *

Answer 1

Let the two digit number = 10x+y

x-y = 3. -------------(1)

Number obtained by interchanging the digits = 10y+x

According to the question:

10x+y+10y+x = 143

11x+11y = 143

11(x+y) = 143

x+y = 143/11

x+y = 13. --------------(2)

From equations (1)&(2) :-

x-y = 3

x+y = 13

2x = 16

x = 8

x-y = 3

8-y = 3

8-5 = y

3 = y

Original number = 10x+y

= 10×5+3

= 53

Answer 2

Answer:

Let the digits of the number be a and b such that the number is (10a+b).

According to the question,

a−b=3 or b−a=3 ...... (1)

10a+b+10b+a=143

a+b=13 ...... (2)

Solving both the equations, we have

a=8 and b=5 or a=5 and b=8

Therefore, the required number is 85 or 58.

Step-by-step explanation:

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