Question

the sum of the digits of a two digit number is 5. the digit obtained by increasing the digit in ten's place by unity is one- eighth of the number. find the number

Answer 1

let the digit in unit place be y and digit in tens place be x
the number will be  10x+y

therefore from first condition x+y=5.......(1)

from second condition x+1=1/8*10x+y
therefore 8x+8=10x+y                8=10x-8x+y                   8=2x+y....................................(2)
now   subtracting  equation  (1) from (2)

  2x+y=8-(x+y)=-5     x   =3now putting  value of x in equation (1)
3+y=5    y=5-3   y  =2 
so the number is 32

Answer 2

Refer to the attachment please.