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The sum of the digits in a two digit number is 10 If the digits are reversed the new number will be 18 more than the original number What is the original number answere?
Wiki User
∙ 13y ago
First you see, two digit no consist of tens place and unit place assume that two digit no be 10x+y
Next sum of those digit is 10 assume it as x+y=10 or x+y-10=0 assume as equation 1
Next question says if you reverse those two digit no (10x+y) it will be 10y+x just changing unit place and tens place. Now as per question
If you reverse, first assumed two digit no . It will be 18 more than the first we assumed two digit
That is 10y+x=10x+y+18
10y-10x+x-y=18
9y-9x=18
9(y-x)=18
Y-x=2 or y-x-2=0 assume it as equation 2
Combine equation 1and 2 that means 1=2
y-x-2=x+y-10
y-y-x-x-2+10=0
-2x+8=0
-2x=-8
X=4 substitute this x in equation 1
x+y=10
4+y=10
Y=6
Sum of these digits that is x+y; 4+6=10
That two digit no 10x+y=10*4+6=46
First we assumed is original no 10x+y that is 46
Original no is 46
Karuna Saravana
Wiki User
∙ 13y agoTo begin with, let's represent the ten's digit with x. Then, we know that the one's digit is (10-x), because the sum of the digits is 10. Since the value of the ten's is 10 times more than the digit, we multiply it by 10. Now we have the original number: 10x+10-x. We can simplify it into 9x+10. For the reversed number, the digits switch spots, so now we multiply the one's by 10. The reversed # is 10(10-x)+x, which could be simplified into 100-9x.To get an equation you have to balance the two sides. For that, you need to add 18 to the original # to make it equal to the reversed #.
9x+10+18=100-9x
9x+9x=100-28
18x=82
x=82/18
x=4
The original number is 46.
The reversed number is 64.
CHECK: 64-46=18
IT WORKS!!!
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