Question

The sum of digits a two-digit number 12 . if the new number formed by reversing the digits is greater than the original number by 54 , find the original number .find the original number . check your solution .
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Answer 1

let a and b the digit
a+b=12 ........(1)
54+(10a+b)=(10b+a)
54+10a+b=10b+a
9a-9b=-54
a-b=-6........(2)
adding (1) and (2)

a+b=12
a-b=-6
----------
2a=6
a=3
so b=9
39+54=93 (verified)
orig no.=39 and  No. when digits reversed=93

Answer 2

Given:

The sum of a two-digit number is 12.

To Find:

The original number

Solution:

Let the two numbers be 'a' and 'b'

It is given that the sum of digits is a two-digit number 12.

Then,

⇒ a + b = 12 ..(i)

It is given that the new number formed by reversing the digits is greater than the original number by 54.

⇒ 54 + (10a + b) = (10b + a)

⇒ 54 + 10a + b = 10b + a

⇒ 9a - 9b = -54

⇒ a - b = -6 ..(ii)

Now, adding (i) and (ii)

⇒ a + b = 12

⇒ a - b = -6

⇒ 2a = 6

⇒ a = 3

So, b = 9

Now, to verify the solution,

39 + 54 = 93

So, the original number is 39 and when it is reversed is 93.