Question

a two digit number is equal to 21 times the difference of its digit if 36 is substracted from the number the position of the digit is reversed . find the number

Answer 1

let the digits be x in tens place and y in ones place
so original no. = y+10x
and 21×|x-y|=y+10x......(1)
y+10x-36=x+10y
9(x-y)=36
x-y=4. x=y+4....(2)
putting value of x in eq. (1)
21×(y+4-y)=y+10y+40
84=11y+40. y=(84-40)÷11
y=4 so x=y+4=8
therefore original no.=4+10×8=84