Question

The sum of digits of two digit number is 13 if the digits are interchanged and the resulting number is added to original number then we get 143 what is the original number

Answer 1

Let the unit digit be xTens digit => x+3x+310(x+3)+x10(x+3)+xdigits interchanged =10x+x+3=10x+x+310(x+3)+x+10x+x+3=14310(x+3)+x+10x+x+3=143=> 10x+30+12x+3=14310x+30+12x+3=143=> 22x+33=14322x+33=14322x=143−3322x=143−3322x=11022x=110x=11022x=11022x=5x=5Original number = 85

Answer 2

solutions:-


Let the number in the digits place be x and the number in the units place be y.

Therefore the decimal expansion is 10x+y.

Given that the digits are interchanged, Then it will become 10y + x.

Given that sum of digits of two digit number = 13.

x + y = 13  ------------------------- (1)


Given that interchanged and resulting number is added to original number, then we get 143

(10x + y) + (10y + x) = 143

10x + y + 10y + x = 143

11x + 11y = 143

x + y = 13  ----------------- (2)


Both (1) & (2) are same.

Case (1) :

4 + 9 = 13

49 + 94 = 143  


Case (2):

5 + 8 = 13

58 + 85 = 143


Case (3):

6 + 7 = 13

67 + 76 = 143


Case (4):

9 + 4 = 13

94 + 49 = 143.


Case (5):

8 + 5 = 13

85 + 58 = 143


Case (6):

7 + 6 = 13

76 + 67 = 143.



Therefore the numbers are 49,58,67,94,76,85

Thanks