GATE Mechanical 2018 Set 1 | GA | Question: 5

Question

A number consists of two digits. The sum of the digits is $9$. If $45$ is subtracted from the number, its digits are interchanged. What is the number?

• A. $63$
• B. $72$
• C. $81$
• D. $90$

Answer 1

Let the two digit number be $xy.$ Its value in decimal is $10x + y.$

Then sum of two digits $=x+y=9 \quad \to(1)$

and $(10x+y)-45=10y+x$          $\{\because yx=10y+x\}$

$10x+y-10y-x=45$

$x-y=5\quad \to (2)$

From the equations $(1)$ and $(2),$ we get $x=7,y=2$

So, the number is $72$

Correct answer: (B).

Answer 2

Number is 72

72 - 45 = 27

so Option B is Correct