Question

A certain number of two digits is three times the sum of its digits, and if 45 be added to it, its digits are reversed. Find the number.

• A. $27$
• B. $86$
• C. $39$
• D. $45$

Answer 1

The correct option is A $27$

Let the one's digit $=x$

Ten's digit $=y$

Number $=10y+x$

$10y+x=3(x+y)$

$10y+x=3x+3y$

$7y=2x\Rightarrow 1$

$10y+x+45=10x+y$

$9x-9y=45$

$x-y=5$

$x=5+y\Rightarrow 2$

Substitute 2 in 1

$7y=2(5+y)$

$7y=10+2y$

$y=2$

$x=5+2=7$

So, the no. is $27.$