Question

A number consistsof two digits. when it isdivided by thesumof digits, thequotient is 6. when the number isdiminished by 9, thedigitsarereversed. find thenumber

Answer 1

Let the unit digit be x
& the ten's digit be y

So, the number be 10x+y

Case 1st
10x+y÷x+y = 6
10x+y = 6(x+y)
10x+y = 6x+6y
10x-6x+y-6y = 0
4x-5y = 0

Case 2nd
Now the digits are interchanged so,
Unit digit = y
& ten's digit = x
According to the question

10x+y-9 = 10y+x
10-x+y-10y = 9
9x-9y = 9
9(x-y) = 9
x-y = 9÷9
x-y = 1
x = 1+y
Now substitute the value of x in equation 4x-5y = 0
4(1+y)-5y = 0
4+4y-5y = 0
4-y = 0
y = 4
x = 1+y
x = 1+4
x = 5
So the number = 10x+y
= 10×5+4
=50+4
=54