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 there places. Find the number.

• A. 40
• B. 52
• C. 28
• D. 36

Answer 1

The correct option is D

36

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)
Let the two digit number be 10y + x.
Number obtained by reversing the digits = 10x + y
Number + 27 = Number obtained by interchanging the digits [Given]
$\therefore$ 10y + x + 27 = 10x + y
$\Rightarrow 9x-9y=27$
$\Rightarrow x-y=3$ . . . . (2)
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
10y + x = 10 $\times$ 3 + 6 = 36
Hence, the number is 36.