Name: General Form of Two and Three-digit Numbers
Uploaded: 2019-07-19
Duration: 58 s
Description: Every number can be expanded into a general form. Click on the play button and know what the general form of a two and a three-digit number is.

Question

The sum of the digits of a $2$ -digit number is $6$ . The number obtained by interchanging its digits is $18$ more than the original number. Find the original number.

Accepted Answer

Let the unit's place of the $2 ‐$ digits number be $b$ and tens place be $a$ .

So, the $2 ‐$ digits number $= 10 a + b$

The sum of the digits of a $2$ -digit number is $6$ .

$a + b = 6$

$\Rightarrow a = 6 - b$ ______________ $(1)$

The number obtained by interchanging the digits $= 10 b + a$

The number obtained by interchanging its digits is $18$ more than the original number.

$(10 a + b) + 18 = 10 b + a$

$\Rightarrow (10 a - a) + (b - 10 b) = - 18$

$\Rightarrow 9 a - 9 b = - 18$

$\Rightarrow 9 (6 - b) - 9 b = - 18$ (From equation $1$ )

$\Rightarrow 54 - 9 b - 9 b = - 18$

$\Rightarrow - 18 b = - 18 - 54$

$\Rightarrow b = \frac{- 72}{- 18}$

$\Rightarrow b = 4$

Substituting the value of $b = 4$ in equation $(1)$ , we get:

$a = 6 - 4 = 2$

Thus, $10 a + b = (10 \times 2) + 4 = 20 + 4 = 24$

Therefore, $24$ is the original number.

The sum of the digits of a $2$ -digit number is $6$ . The number obtained by interchanging its digits is $18$ more than the original number. Find the original number.

Important Questions on Playing With Numbers

Learn and Prepare for any exam you want !

The sum of the digits of a 2-digit number is 6. The number obtained by interchanging its digits is 18 more than the original number. Find the original number.

Important Questions on Playing With Numbers

Learn and Prepare for any exam you want !

The sum of the digits of a $2$ -digit number is $6$ . The number obtained by interchanging its digits is $18$ more than the original number. Find the original number.