Question

the sum of the digit of a two digit number is 13 . the number obtained by interchanging its digits exceed the given number by 9. find the original number

Answer 1

Let two digit no. be a 10x + y

x + y = 13 eq1

10y + x = 10x + y + 9

9y - 9x = 9

y - x = 1 eq2

Adding eq1 and eq2

2y = 14

y = 7

Put value of y in eq1

x + 7 = 13

x = 13 - 7 = 6

Number is 10x + y

10 × 6 + 7

= 67 Answer


Thanks

Answer 2

Let the number be xy

Sum of digits =>

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

Interchanged number =>

10y + x = 10x + y + 9
9y - 9x = 9

y - x = 1.......(2)

From (1) & (2)

y + x = 13
y - x = 1

2y = 14
y = 7

x = 6

So, number is 67