Question

Eight times a two digit number is equal to three times the number obtained by reversing the order of its digits. If the differences between the digit is $5$, find the number.

Answer 1

Let one's digit$=y$

Units digit$=x$

Number$=10x+y$

$\Rightarrow 8(10x+y)=3(10y+x)$

$\Rightarrow 80x+8y=30y+3x$

$\Rightarrow 77x=22y$

$\Rightarrow 7x=2y---\left(1\right)$

Also, $x-y=5---\left(2\right)$

from eq(1) and (2)

$\Rightarrow x-y=5$

$\Rightarrow x+\frac{2y}{7}-y=5$

$\Rightarrow 2y-7y=35$

$\Rightarrow -5y=35$

$\Rightarrow y=-7$

$\Rightarrow x-y=5$

$\Rightarrow x+y=5$

$\Rightarrow x=-2$

Number$=-27$

or

$\Rightarrow y-x=5$

$\Rightarrow y-\frac{2y}{7}=5$

$\Rightarrow 5y=35$

$\Rightarrow y=7$

$\Rightarrow 7-x=5$

$\Rightarrow x=2$

Number$=27$