Question

There is a certain number consisting of two digits, to the sum of whose digits if we add 7, the result will be 3 times the left hand digit, and if from the number itself we subtract 18 the digits will be reversed. The number is

• A. $47$
• B. $52$
• C. $61$
• D. $63$

Answer 1

The correct option is D $63$

As the number is a two digit , then let $x$ be tens's place and $y$ be one's place.

$\therefore$ The two digit number would form as $10x+y$

According to the question,

A number consisting of two digits is $7$ times the sum of its digits.

$\Rightarrow$ $10x+y=7(x+y)$

$\Rightarrow$ $3x-6y=0$

$\Rightarrow$ $x=2y$ ------ ( 1 )

When $27$ is subtracted from the number the digits are reversed.

After reversing the digits, the number $=10y+x$

$\Rightarrow$ $(10x+y)-27=10y+x$

$\Rightarrow$ $9x-9y=27$

$\Rightarrow$ $x-y=3$ .......(2)

Substituting the value of $x$ from equation ( 1 ) to equation ( 2 ) , we get

$\Rightarrow$ $2y-y=3$

$\Rightarrow$ $y=3$

$\Rightarrow$ $x=2y$

$\Rightarrow$ $x=2\left(3\right)=6$

$\therefore$ The number is $=10\left(6\right)+3=63$