Question

the sum of digits of a two digit number is 10.On reversing the digits,the new number formed is one less than two times the original number. Find the original number
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Answer 1

Answer:

1st no. = -79/27

2nd no. =  -349/27

Step-by-step explanation:

let 1st no. be x,

therefore 2nd no.= 10 - x

the no. is = 10x + 10-x = 9x + 10

when digits are reversed, no. = (10 - x)10 + x = 100 - 10x + x = 100 - 9x

according to the problem,

new number = 2(original no.) + 1

or, 100 - 9x = 2(9x + 10) + 1

or, 100 - 9x = 18x + 20 + 1

or, 100 - 9x = 18x + 21

or, -9x - 18x = 21 - 100

or, -27x = 79

or, x = -79/27

and, x-10 = -79/27 -270/27 = -349/27