Question

i have 50 points points plzzz answer this question
the sum of the digits of a two digit number is 12 . If the number formed by reversing
the digits is greater than the original number by 54 . find the original number .

Answer 1

Hey

Here is your answer,

Let the two digit number be 10x + y
Given that sum of the digits = 12
Therefore x + y = 12 (Equation 1)

Also given that if the number is reversed, the new number exceeds the original number by 54.
Therefore
10y + x = 10x + y = 54
9x - 9y = - 54
Taking 9 as common
x - y = - 6 (Equation 2)

Adding equation 1 and 2
x + y = 12
x - y = - 6

2x = 6
x = 3

3 + y = 12
y = 9

The original number is 10(3) + 9 = 39.

Hope it helps you!

Answer 2

Hey mate!

Here's your answer!!
____________________

Let the digit at one's place be x and ten's place be (12-x)

∴ The number
= 10 (12-x) + x
= 120 - 10x + x
= 120 - 9x

Now, the number obtained by interchanging the digits is,

= 10x + 12 - x
= 9x + 12

Now, it is given in the question that,

9x + 12 = 54 + 120 - 9x

∴ 9x + 9x = 174 - 12

∴ 18x = 162

∴ x = 162/18

∴ x = 9

Therefore, the number is
= 120 - 9x
= 120 - 9(9)
= 120 - 81
= 39.
_____________________
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