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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?

  1. 63
  2. 72
  3. 81
  4. 90
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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).
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