Question

In a two-digit number, ten's digit is twice the unit's digit. The number formed by interchanging the digits is $36$ less than the original number. The original number is _________.

• A. $48$
• B. $70$
• C. $72$
• D. $84$

Answer 1

The correct option is D $84$

Let $XY$ be the two digit number

$X=2Y$ ..........(1)

Number formed by exchanging the digit is $YX$.

$YX=XY-36$ ...........(2)

Expanding the two digit numbers

$10Y+X=10X+Y-36$ .........(3)

$\Rightarrow 9(Y-X)=-36$

Substituting from (1), we get

$\Rightarrow Y=4$

and $X=8$

So, the number is 84.