Question

the sum of two digit number and number obtained on reversing the digit is 99if the digits. differ by 3 find number

Answer 1

$\color{purple}{Solution:}$

Let the digit at unit's place be x and that at ten’s place be y .

Original number = 10y + x

Reversed number = 10x + y

Now,

$\bold{\boxed {A.T.Q.}}$

10y + x + 10x + y = 99

»» 11y + 11x = 99

»» 11( x + y ) = 99

»» x + y = 9.........(i)

Also, x - y = ± 3

When x - y = 3 ---------------- (ii)

and x + y = 9

On adding (i) and (ii) , we get

x + y + x - y = 9 + 3

2x = 12

•°• x = 6

From (i) we get

x + y = 9

6 + y = 9

y = 3

Original number = 10y + x

=> 10 × 3 + 6

=> 30 + 6

=> 36

When x - y = -3 ------------------ (iii)

Adding (i) and (iii) we get ;

2x = 6

•°• x = 3

and from (1) we get y = 6

Original number = 10y + x

=> 10 × 6 + 3

=> 60 + 3

=> 63

Hence the number is 36 or 63.

$\color {purple}{Thank you}$