Question

A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is $18$ less than the original number. The number is

• A. $28$
• B. $39$
• C. $42$
• D. $49$

Answer 1

The correct option is C $42$

$10x+y=7(x+y)=7x+7y$
or $10x-7x=7y-y$
or $3x=6y$
or $x=2y$ ........(1)
Number formed by reversing the digits is yx, i.e.,
$10y+x=10x+y-18$
Substituting $x=2y$, we get
$10y+2y=10\times 2y+y18$
or $2y=21y-18$
or $21y-12y=18$
or $9y=18$
or $y=2$
$\therefore x=2y=2\times 2=4$
Therefore, the number is 42.