Question

The sum of the digits of a two digit number is $6$. The digit obtained by increasing the digits in ten's place by unity is one-eighth of the number, then the number is

• A. $18$
• B. $23$
• C. $35$
• D. $15$

Answer 1

The correct option is B $23$

Let the digit in unit place be $y$ and digit in tens place be $x$.

The number will be $10x+y$

Therefore, from first condition $x+y=6$ $............\left(1\right)$

From second condition

$x+1=\frac{1}{8}(10x+y)$

Therefore,

$8x+8=10x+y$

$2x+y=8$ $..........\left(2\right)$

Now, subtracting equation $\left(1\right)$ from $\left(2\right)$, we get

$x=2$ and $y=3$

Therefore, the number is

$=10\times 2+3=20+3=23$