Question

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 numbers​

Answer 1

Answer:

There you go

Step-by-step explanation:

Let x = the 10's digit, and y = the units digit

Write an equation for each statememt

:

"sum of the digit of two digit no. is 12."

x + y = 12

or

y = 12 - x; we use this for substitution, if needed

;

"the given no. exceed the no. obtained by interchange the digit by 36."

:

Given number: 10x + y

interchanged number: 10y + x

:

The equation from the given statement:

10x + y = 10y + x + 36

Some simple algebra:

 

10x - x = 10y - y + 36

9x = 9y + 36

Simplify, divide equation by 9

x = y + 4

:

Substitute (12-x) for y, (from the 1st statement)

x = (12-x) + 4

x + x = 12 + 4

2x = 16

x = 8

:

y = 12 - 8 = 4

:

Our number is 84:

:

:

Check it: 84 - 48 = 36

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Answer: 84

Step-by-step explanation:

Let ones place = x

Tens place = y

number will be = 10y +x

Number after reversing the digits = 10y +x

According to question:

x+y = 12  ⇒ x= 12- y  ------(i)

(10y+x) -36 = 10x+y

⇒ 10y +x -10x-y =36  ⇒ 9y  - 9x=36 ⇒ y-x=4   ----(ii)

Put the value of (i) in (ii)

y-(12-y)= 4 ⇒ y-12+y = 4 ⇒ 2y= 16 ⇒ y= 8  x= 4

Given number is 10y+x = 10 x 8+4 = 84

Hence, the number is 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

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