Question

a number conists of two digits where the number is divided by the sum of its digits the qoutient is 7 if 27 is subtracted from the number the digits interchange their places find the number

Answer 1

Let the Digit at ones place be y and tens place be x.

Therefore , According to Question , When we form equation it is →

(10x+y)/x+y = 7

or, 10x+y = 7(x+y)

or, 10x + y = 7x + 7y

or, 10x - 7x = 7y - y

or, 3x = 6y

or, x = 6y/3......................1

Then , when we subtract 27 from the number , the digits are interchanged.

→ 10x+y -27 = 10y + x.............2

Substitute value of x from 1 and put it in 2 →

10(6y/3)+y -27 = 10y + 6y/3

or, 60y/3 + y - 27 = (30y+6y)/3

or, (60y+3y)/3 - 27 = 36y/3

or, 63y/3 - 36y/3 = 27

or, 27y/3 = 27

or, 27y = 27×3

or, y = (27×3)/27

or, y = 3

Therefore ,

x = 6y/3

or, x = 6(3)/3

or,x = 6

Therefore ,

10x + y = 10(6) + 3

= 63

Verification →

63/(6+3) = 63/9 = 7

63 - 27 = 36
________________

Answer → Our Number is 63
______________________________