Question

the sum of a two digit number and the number obtained by reversing the order of its digit is 99.If the digits differ by 3,find the numbers

Answer 1

Given :

• The sum of a two digit number and the number obtained by reversing the order of its digits is 99.

• The digits differ by 3.

To find :

• The number =?

Step-by-step explanation :

Let the 2 digits be of the m , m. respectively

➛ 2 digit number = 10m + n.

2 digit number obtained by ususing the digit

= 10n + m

∴ ( 10m + n ) + ( 10n + x ) = 99

⇒11m + 11n = 99

⇒ m + n = 9 .................. ( 1 )

By the second condition,

➛ m - n = 3 ................... ( 2 )

On adding equation ( 1 ) and ( 2 )

m + n + m - n = 9 + 3

2m = 12

m = 12/2

m = 6

On putting m = 6 in ⟶ equation ( 1 )

6 + n = 9

n = 9 - 6

n = 3

Hence, Number is :

➞ 10m + n = 63

or ,

➞ 10n + m = 36.

Therefore, The number is 63 or 36.