Question

the the sum of digit in a two digit number is 8 the number got by Inder changing the digit is 18 more than the original number find the number ​

Answer 1

Step-by-step explanation:

Let the ones - digit no. = x

So, tens- digit no. = (8 - x)

Therefore,

Original no. = x(1) + (8 - x)10

= x + 80 - 10x

= 80 - 9 x

When digits get interchanged ,

New no. = x(10) + (8 - x)1

= 10x + 8 - x

= 8 + 9x

Now , when interchanged, the new no. is 18 more than original no. ------

So, New no. - Original no. = 18

=> 9x + 8 - (80 - 9x) = 18

=> 9x + 8 -80 + 9x = 18

=> 18x - 72 = 18

=> 18 x = 18 + 72

=> 18x = 90

=> x = 90 / 18

=> x = 5

So,

Original no. = 80 - 9(5)

= 80 - 45 = 35

Therefore ,

New no. = 53

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