Question

The sum of the digit of a two digit number is 15. If the number formed by reversing the digits is less than the original number by 27, find the original number.

Answer 1

$<I>Solution:$

Let units place digit be x

then, tens place digit = 15 - x

Number formed :

= 10 ( 15 - x ) + x

= 150 - 10x + x

= 150 - 9x

Reversed number formed :

= 10x + 15 - x

= 9x + 15

It is given that :

9x + 15 = 150 - 9x - 27

=> 9x + 9x = 150 - 27 - 15

=> 18x = 108

=> x = 108/18 = 6

Thus, original number formed:

= 150 - 9 (6)

= 150 - 54

= 96

$<I>[ANSWER: 96]$

Answer 2

ANSWER

96

Step By Step Explanation

Here, let the one's digit be x and tens digit be y respectively.

So, We know that =>

x + y = 15(Sum of digits). -----(i)

And, we know that the original number is

=> 10y + x.

On reversing the digit the number we will get is

=>10x + y.

Also, we know that :>

Original number - Reversed number = 27

=> 10y + x - (10x + y) = 27

=> 10y + x - 10x - y = 27.

=> 9y - 9x =27

=> 9(x-y) = 9 × 3

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

So, on adding equation (i) and (ii) we get>

x + y = 15

x - y = 3 (Adding)

_____________________

2x = 18

=> x = 9.

Putting x = 9 in equation (i) we get =>

9 + y = 15

=> y = 6.

So the number is 96.