Question

The sum of the digits of a two digit number is 16.The number obtained by interchanging the digits is less by 18 than the original number. Find the two digit number (Please Give The Answer With Sentences eg.Substituting x in equation 1)​

Answer 1

Step-by-step explanation:

Let no. at ones place be x.

Let no. at tens place be y .

ATQ,

x+y=16

y=16-x ----------eq(1)

orignal number be x+10y.

interchanged number y+10x.

x+10y-(y+10x)=18

x+10y-y-10x=18

9y-9x=18

y-x=2

Multiply both sides by -1.

x-y=-2 ----------eq(2)

Putting the value of y using equ(1) in eq (2)

x-(16-x)=-2

x-16+x=-2

2x=16-2

x=7

Putting the value of x in eq (2).

x-y=-2

7-y=-2

-y=-2-7

y=5

So, The Original Number is

x+10y=7+50=57

Number after interchanging digit is

y+10x=5+70=75