Question

The sum of the digits of a two-digit number is $9$. If $9$ is added to the number, then its digits interchange their place. What is the difference in cube of the digits?

• A. $65$
• B. $61$
• C. $89$
• D. $125$

Answer 1

Answer: (B)

Let the number be ab

Given sum of digits is $9\Rightarrow a+b=\mathrm{9...}\left(1\right)$

If 9 is added, its digits interchange which means ba

$10a+b+9=10b+a$

$\Rightarrow 9a+9=ab$

$\Rightarrow a-b=-\mathrm{1...}\left(2\right)$

From (1) & (2), $a=4,b=5$

$\therefore$ Diference in cube of digits $=125-64$

$=61$