Question

The sum of the digits of a two digit number is 15.The number is decreased by 27,if the digits are reversed.Find the numbers.

Answer 1

Let us assume, x and y are the two digits of a number
Therefore, The two digit number is = 10x + y and the reverse number is 10y + x
Given:
x + y = 15 ---------1
y = 15 - x
Also given:
10x + y - 27 = 10y + x
9x - 9y = 27
x - y = 3  -----------2
Adding equation 1 and 2
2x = 18
x = 9
Therefore, y = 15 - x = 15 - 9 = 6
The two digit number is = 10x + y = (10 * 9) + 6 = 96
And the reverse number = 10y + x = (10 * 6) + 9 = 69

Answer 2

Let the digit in the units place be x.

Then, the digit in the tens place = (15 - x)

> Original number = 10 * (15 - x) + x

= (150 - 9x).

On reversing the digits, we have x at the tens place and (15 - x) at the units place.

> New Number = 10x + (15-x) = (9x+15).

Now, (9x+15) - (150 - 9x) = 27

> 135 - 18x = 27

> 18x = (135 - 27)

> x = (108/18) = 6

Hence, the original number is 96