The sum of the digits of a two - digit number is 4 . The number got by interchanging the digits is 18 less than the original number . what is the number . ?
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The sum of the digits of a two - digit number is 4 . The number got by interchanging the digits is 18 less than the original number . what is the number . ?
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Verified answer
[tex]\huge\mathfrak\red{Answer:-}[/tex]
31
[tex]\mathfrak\purple{Step \: by \: stiep \: explanation:-}[/tex]
x + y = 4
10x + y - 18 = 10y + x
9x - 18 = 9y
x - y = 2
x + y = 4
x - y = 2
thus, 2x = 6 orx = 3
x - y = 2
3 - y = 2
y = 1
so, number is 10(3) + 1 or 31
_divide by 9
check
13( digits interchanged) is 18 less than 31
Answer:
Step-by-step explanation:
Given,
To Find,
Solution,
Let's,
And,
The Original Number = 10x + y
After Interchanging the Digits,
And,
The Interchanged number = 10y + x
According To Question,
Situation 1,
The sum of digits is 4.
So,
[tex]:\implies\tt x + y = 4 \: \: \: ...(1)[/tex]
Situation 2,
[tex]:\implies\tt (Original \: \:Number) - (Interchanged \: \: Number) = 18 \\ \\ :\implies\tt (10x + y) - (10y + x) = 18 \\ \\ :\implies\tt 9x - 9y = 18 \\ \\ :\implies\tt x - y = 2 \: \: \: ...(1) [/tex]
By Elimination Method,
Adding Eq [1] and Eq [2] to eliminate y,
[tex]:\implies\tt (x + y) + (x - y) = 4 + 2 \\ \\:\implies\tt x + y + x - y = 6 \\ \\ :\implies\tt 2x = 6 \\ \\ :\implies \color{red} \boxed{\tt x = 3}[/tex]
Substituting this value of x in Eq [1],
[tex]:\implies\tt x + y = 4 \: \: \: ...(1) \\ \\ :\implies\tt 3 + y = 4 \\ \\ :\implies \color{red} \boxed{\tt y = 1}[/tex]
Hence, x = 3 and y = 1
The Original Number = 10x + y
Required Answer,