Question

# The one’s digit of a two digit number is double the digit in ten’s place. If the sum of the digits is $9$ . Find the number.

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Hint: The two digit number can be expressed as number=[ (digit at tens digit×$10$) +digit at one’s place]. So, we can assume the digit at ten’s place to be x. Since the digit at one’s place is double the digit at ten’s place we can assume it to be$2{\text{x}}$ .We are give the sum of both digits=$9$ .On putting the values in the formula we can solve for x and find the digits.Then we can express the digits in number.

We are given that, in a two digit number the one’s digit is double the digit in ten’s place. The sum of the digits is $9$ . Let us assume that the ten’s digit is x then the one’s digit will be $2{\text{x}}$.
Then according to the question, sum of digits= $9$
$\Rightarrow {\text{x + 2x = 9}}$
On solving we get,
$\Rightarrow 3{\text{x = 9}} \Rightarrow {\text{x = }}\dfrac{9}{3} = 3$
Now we know the ten’s digit =x= $3$ then we can find the one’s digit.
One’s digit= $2{\text{x}}$=$2 \times 3 = 6$
Now we can express the two digit number as-
$\Rightarrow$ Number =ten’s digit ×$10$ + one’s digit
Here we multiplied the ten’s digit by $10$ because it is in tenth’s place in the number.
On putting the value of the digit we get,
$\Rightarrow$ Number=$\left( {3 \times 10} \right) + 6$
On solving we get,
$\Rightarrow$ Number=$30 + 6 = 36$
So the number is $36$ .

Note: Here, the student may get confused when he puts the digits value in the expression- Number =ten’s digit ×$10$ + ones digit. He/she may directly add the numbers as-tens digit + ones digit which is wrong as it will not give us a two digit number. To get a two digit number we multiply the ten’s digit by $10$ as the digit is in tenth place( which is its place value).Similarly we can express a three digit number as-
Number= ($100$ ×hundred’s digit)+ (ten’s digit ×$10$) + one’s digit
See here we multiplied the hundred’s digit with $100$ because it is a place value of hundred’s digit.