Question

A number consist of two digits, the difference of whose digits is $5$. If $8$ times the number is equal to $3$ times the number obtained by reversing the digits, Find the number.

Answer 1

let number is $xy$, where $x$ is ten's place and $y$ is unit place

so it can be written as $(10x+y)$

given that $|x-y|=5$

that is $x-y=+5........eq\left(1\right)$

or $x-y=-5.........eq\left(2\right)$

Now,

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

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

$77x-22y=0$

$7x-2y=0........eq\left(3\right)$

solving $eq\left(1\right)$ and $eq\left(3\right)$

$7x-2y=0$

$-(2x-2y=10)$

it gives $5x=-10$

hence $x=-2$

put in eq(1)

$-2-y=5$

$y=-7$

so number$,10x+y=10(-2)+(-7)$

$N=-27$

solving eq(2) and eq(3)

$7x-2y=0$

$-(2x-2y=-10)$

it gives $,5x=10$

$x=2$

put in eq(1)

$2-y=-5$

$y=7$

so$,N=10x+y=10\ast 2+7$

$N=27$