Question

A number Consist of two digits.when number Is divided by the sum of its digits,the quotient is 7.if 27 is subtracted from the number The digit interchange their places .find number?

Answer 1

let unit digit=x
tens digit=y
number=10y+x
(10y+x)/x+y =7 (1)
10y+x-27=10x+y
9y-9x-27=0
y-x-3=0
from (1) 10y+x=7x+7y
3y=6x
y=2x
2x-x-3=0
x=3,y=6
number=63

Answer 2

Answer:

Let digit at ten's place be x

And digit at one's place be y

Number = 10x + y

Acc. to ques.

1st case.

10x + y / x + y = 7

10 x + y = 7x + 7y

10x - 7x + y - 7y = 0

3x - 6y = 0

x - 2y = 0 ----------(1)

2nd case

(10x + y) - 27 = 10y + x

10x + y - 27 = 10y + x

10x - x + y - 10y = 27

9x - 9y = 27

9(x - y) = 9 (3)

x - y = 3 ----------(2)

Now,

Subtracting (1) and (2)

x - 2y = 0

x - y = 3

- + -

___________

-y = -3

y = 3

Put y = 3 in (2)

x - 3 = 3

x = 3 + 3

x = 6

Number becomes = 10x + y

= 10×6 + 3

= 63