Question

A two digit number is four times the sum of its digits. if 27were added to the number, it becomes seven times the sum of digits. find the number

Answer 1

2 digit no = 10y+x
sum of digits= y+x
10y+x=4(y+x)
10y+x= 4y+4x
4y+4x-x-10y=0
3x-6y=0
x-2y=0 ...............(i)
x=2y

10y+x+27= 7(y+x)
10y+x+27= 7y+7x
7x+7y-10y-x-27=0
6x-3y-27=0
2x-y-9=0 ............(ii)
2x2y-y-9=0
4y-y=9
3y=9
y=3
x=2y= 6
no will be= 10y+x= 10x3+6= 36 Ans