Question

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. Find the original number.

Answer 1

Hence the original number is 13.

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.

Answer 2

Original number = 31

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'.
`\Rightarrow y=3x`

Situation 2- 'If the digits are reversed, the new number is 18 more than the original number'.

`\Rightarrow 10y+x=10x+y+18`

Now, we solve the situation 2,

`10y+x=10x+y+18`

`9y-9x=18`

`9(y-x)=18`

`y-x=2`

Put value of y from situation 1, y=3x

`3x-x=2`

`2x=2`

`x=1`

Put back in situation 1,

`y=3x\Rightarrow y=3(1)=3`

Therefore, x=1 and y=3 so, the number is 30+1=31

Original number = 31