Question

A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number.

• A. 25
• B. 45
• C. 75
• D. None of these

Answer 1

The correct option is C 75

Let the tens and the units digits in the number be x and y, respectively.
So, the number may be written as $10x+y$.
According to the given condition.
$10x+y=6(x+y)+3\Rightarrow 4x-5y=3$ .....(i)
If we interchange the digits of Original number then we get new number. i.e $10y+x$
According to the given condition
$10y+x+18=10x+y$
$\Rightarrow 9x-9y=18\Rightarrow x-y=2$ .....(ii)
Now multiplying equation (ii) by $4$. we get,
$4x-4y=8$ ....(iii)
On subtracting (iii) from (i). we get,
$4x-5y-(4x-4y)=3-8$
$\therefore y=5$
On substituting $y=5$ in (ii). we get,
$x-5=2\Rightarrow x=7$
$\therefore$ number is $10x+y=10\left(7\right)+5=75$