Sum 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
Answers
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
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