the sum of the digits of a two-digit number is 8 the number obtained by reversing the digits is 36 more than the original number find the number
Answers
Answer:
If the number obtained by interchanging the digits of a 2-digit number is 36 more than that the original number and the sum of the digits is 8, then what is the original number?
Hi!
So, let x be the ten's digit of our number.
The sum of the digits= 8
Therefore, one's digit is definitely 8-x.
Now, the original number is=
10(x)+(8-x)
Since x is in the ten's place. For example if x was 3 and 8-x was five. The number would be 35.
And 10(3)+ (8–3) = 30+5= 35.
Moving on from the example world to the real world,
10(x)+(8-x)= 9x+8
So this is our original number.
The question says that the new number is formed after interchanging the digits.
So in the new number, ten's digit is 8-x and on' digit is x.
So the new number is 10(8-x)+(x)
=80–9x
And they have also said that the new number is more than the original number by 36. So,
New number-36= original number
So,
80–9x -36= 9x+8
-9x+44= 9x+8
Transposing +8 to LEFT HAND SIDE((LHS)),
-9x+44–8=9x
Transposing -9x to RIGHT HAND SIDE((RHS)),
44–8=9x+9x
36=18x
Transposing *18 to LHS
36/18=x
Therefore, x= 2 and 8-x= 8–2= 6
Therefore the original number is 26.
New number= 62( interchanging the digits )
62–36= 26
So, recheck done.
Therefore, original number= 26
Answer:
26
Step-by-step explanation:
62-36=26
so, 26 is answer