Question

The sum of a two digit number is 15.if the number formed by reversing the digits is less than the original number by 27,find the original number.

Answer 1

$let \: the \: units \: place \: be \: x \: then \: the \: digit \: in \: the \: tens \: place \: = 15 - x \\ the \: original \: number = 10 \times (15 - x) + x = 150 - 9x \\on \: reversing \: the \: digits \\ the \: new \: number = 10x + (15 - x) = 9x + 15 \\ (150 - 9x) - (9x + 15) = 27 \\ - 18x = 27 + 15 - 150 \\ - 18x = - 108 \\ 18x = 108 \\ x = 6 \\ the \: digit \: in \: the \: units \: place = 6 \\ the \: digit \: in \: the \: tens \: place = 15 - 6 = 9 \\ the \: original \: number = 96$

Answer 2

Answer:

let the two digit of the no. be x and y

also,

sum is given as 15

10x+y=15.......(i)

now,

no. formed by reversing the digit,

10y+x

it is less than original no. i.e.10x+y by 27

therefore,

10y+x=10x+y- 27

=>10y-y=10x-x-27

=>9y=9x-27

=>9x-9y=27

=>x-y=3....(ii)

solve the two eq. u'll get ans

s