Question

The sum of the digits of a 2-digit number is 12. The given number exceeds the number obtained by interchanging the digits by 36. Find the number. ​

Answer 1

The sum of a the digits of a 2-digit number is 12. If the digits are interchanged, the new number exceeds the old number by 36. What is the number?"

Let's represent the number as 10*a + b, and the number with the digits reversed as 10*b + a.

We know that

a + b = 12 (1)

and that

10 * b + a = 10 * a + b + 36 (2)

So

9 * b - 9 * a = 36

b - a = 4 (3)

Adding (1) and (3):

2 * b = 16 => b = 8

From (1), a = 4

So our initial number is 48 and the digits-reversed number is 84:

48 + 36 = 84.

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Answer 2

Answer:

$\huge\star{\red{Q}{uestion}}\star\:$

Sum of the digits of a two-digit number is 12. The given number exceeds the number obtained by interchanging the digits by 36. Find the given

number.

$\huge\star{\red {A}{nswer}}\star\:$

$\huge\underline {Let,}$

The tens digit of the required number be x

and the units digit be y

\huge\underline {Then,}

Then,

x + y = 12 ......... eq. (1)

Required number = (10x + y)

Number obtained on reversing the digits = (10y + x)

$\huge\underline {Therefore,}$

(10y + x) - (10x + y) = 18

9y - 9x = 18

x - y = 12 ......... eq. (2)<br>

On adding eq. (1) and eq. (2)

$\huge\underline {We\: get}$

x + y + y - x = 12 +2

2y = 14

y = 2

$\huge\underline {Therefore}$

x = 5

Hence, the required number is 57

$\huge\green { Hope\: this\: helps\: you}$