Answer:
Original number = 31
Step-by-step explanation:
Given : The ones digit of a number is 3 times the tens digit. If the digits are reversed, the new number is 18 more than the original number.
To find : The original number.
Solution : Let x = 10's digit and y= unit digit
Then the original number = 10x+y
Situation 1 - 'The ones digit of a number is 3 times the tens digit'.[tex]\Rightarrow y=3x[/tex]
Situation 2- 'If the digits are reversed, the new number is 18 more than the original number'.
[tex]\Rightarrow 10y+x=10x+y+18[/tex]
Now, we solve the situation 2,
[tex]10y+x=10x+y+18[/tex]
[tex]9y-9x=18[/tex]
[tex]9(y-x)=18[/tex]
[tex]y-x=2[/tex]
Put value of y from situation 1, y=3x
[tex]3x-x=2[/tex]
[tex]2x=2[/tex]
[tex]x=1[/tex]
Put back in situation 1,
[tex]y=3x\Rightarrow y=3(1)=3[/tex]
Therefore, x=1 and y=3 so, the number is 30+1=31
Original number = 31
Answer:
Hence the original number is 13.
Step-by-step explanation:
Let us consider the ten's digit to be x.
so the one's digit will be 3x( as it was given the one's digit of a number is 3 times the ten's digit ).
so the number could be represented as x 3x or it can also be represented as: 10x+3x=13x
after reversing the number the number becomes: 3x x
or it can also be represented as: 3x×10+x=30x+x=31x
now the new number is 18 more than the original number, that means:
31x=13x=18
18x=18
x=1
Hence the original number is 13.
and the reversed number is 31.
