Question

In a two-digit number, the units digit is twice the ten's digit. Also, if 27 is added to the number, the digits interchange their places. Find the number. $\left[3\text{Marks}\right]$

Answer 1

Let the digit in the units place be x and digit in the tens place be y.

Units digit = twice the tens digit [Given]
$\Rightarrow$ x = 2y . . . . (1) $\left[0.5\text{Marks}\right]$

Also, the two-digit number will be 10y + x. $\left[0.5\text{Marks}\right]$

Therefore the number obtained by reversing the digits = 10x + y

Given that if 27 is added to the number, the digits interchange their places.

$\Rightarrow 10y+x+27=10x+y$
$\Rightarrow 9x-9y=27$
$\Rightarrow x-y=3$ . . . . (2) $\left[1\text{Mark}\right]$

Putting x = 2y in equation (2), we get,
2y - y = 3 $\Rightarrow$ y = 3

Putting y = 3 in equation (2), we get,
x - 3 = 3 $\Rightarrow$ x = 6

Substituting the values of x and y to get the number,
$⟹$10y + x = 10 (3) + 6 = 36 $\left[1\text{Mark}\right]$

Hence, the number is 36.