Question

The sum of the digits of a two-digit number is $5$. The digit obtained by increasing the digit in tens' place by unity is one-eighth of the number. Then the number is

• A. less than $30$
• B. lies between $30$ and $40$
• C. more than $37$
• D. lies between $40$ and $50$

Answer 1

Answer: (B)

lies between $30$ and $40$

$x+y=5$
and $x+1=\frac{1}{8}(10x+y)$ .........(1)
or $8x+8=10x+y$
or $2x+y=8$ .........(2)
Subtract equation (1) from equation (2)
$2x+y=8$
$+x+y=5$
$\underset{–}{(-)(-)(-)}$
$x=3$
$\therefore y=2$
Number is $32$.