Question

the ratio of tens to the unit digit is 2:3. if 27 is added to the number, the number interchange their places find the number

Answer 1

hi

The ratio of tens to the unit digit is 2:3
tens plce = t


units = u

t/u = 2/3

tens place = 2u/3

 if 27 is added to the number, the number interchange

10t + u +27 = 10u +t

10t + u -10u - t = 27

9t - 9u = 27

t - u = 3

since 

t - u = 3

t = 2u/3

2u/3 - u = 3

1/3u = 3

u = -3*3

u = 9 (remove - sign)

now,

t=2u/3

2*9/3

t = 6

so number is 69

hope it helps u

:)

Answer 2

let ten,s be x and unit digits be y ,we have
the number =x+y..1, required number=10x+y
reversing number =10y +x
there for,(10y+x)-(10x+y)=27
=9y-9x=27
=9(y-x)=9(3)
=y-x=3
y=3+x
put y=3+x in eq...1
=x+3+x
2x=-3
x=-3/2
put x=-3/2in eq..1
-3/2+y
y=3/2
hence number be- 3/2+3/2=0/2=0

hope it helps you