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 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


Hope this helps!

Answer 2

Hey mate..
========

Let , the digits in the unit place be x And the digits in the tens place be y.

•°• The number is 10y + x

It is given that , The sum of the digit of the two digit number is 13.

Which means,

=> x + y = 13......(1)

Also,

When the digits are interchanged and the resulting number is added to original number then we get 143.

Which means,

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

=> 10y + y + 10x + x = 143

=> 11y + 11x = 143

=> 11 ( y + x ) = 143

=> y + x = 143 / 11

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

Both (1) and (2) are same.

Case 1 :-
======

▪ 9 + 4 = 13

▪ 94 + 49 = 143

Case 2 :-
=======

▪ 5 + 8 = 13

▪ 58 + 85 = 143

Case 3:-
======

▪6 + 7 = 13

▪67 + 76 = 143

Case 4 :-
======

▪4 + 9 = 13

▪49 + 94 = 143

Case 5 :-
=======

▪8 + 5 = 13

▪85 + 58 = 143

So,

The numbers are as follows :-

94 , 58 , 67 , 49 and 85

Hope it helps !!