Question

the sum of the digits of a two digit number is 12 the number obtained by interchanging the digits exceeds the original number by 54 find the original number

Answer 1

let the tens place digit be 'x'and in unit place be'y'. therefore the no is 10x+y


according to the condition,
x+y = 12 or x= (12-y)

now the digit in unit place is x and tens place is y
therefore the no is (10y+x)

by the condition

10y+x = 10x+y+54

or 9x - 9y +54 =0

or 9(x - y + 6) =0

or 12-y - y+6 =0

or -2y +18 =0

or 2y=18

or y=9

therefore x= 12 -y
= 12-9= 3

therefore the original no is 10x +y =10*3+9=39

Answer 2

Answer:

step by step

let digit at one's place =x

therefore digit at tens place = (12-x)

original no. x+10(12-x)

x+120-10x

120-9x

on interchanging the digit

digit at one's place (12-x)

digit at tens place x

new number=10(12-x)+1(x)

9x+120

A.T.Q

new no - original no.

(9x+120) - (120-9x)

original no 39