Question

The sum of the digits of a $2$-digit number is $9$. The number is $6$ times the units digit. Find the number.

Answer 1

Let the digit in the units place $=x$

Let the digit in the tens place $=y$

Then the 2-digit number is $=10y+x$

Sum of the digits of the number is $9$

$x+y=9$ ....................... (1)

The number is $6$ times the units digit.

So,

$10y+x=6x$

$10y=5x$

$2y=x$ ....................... (2)

Substitute $x=2y$ in equation (1),

$2y+y=9$

$3y=9$

$y=3$

$x=2y$

$x=2\times 3=6$

Now, the number is $=10y+x$

$=30+6$

$=36$