Question

The sum of the digit of two number is 9 the number is 6 times the units digit find the number

Answer 1

Let the ten's digit and one's digit be x and y respectively.

Given

$x+y = 9\\10 x + y = 6y$

Now,

$x+y = 9\\\implies y = 9-x$

Substituting y in the second equation, we get,

$10x+9-x=6(9-x)\\\implies 9x+9 = 54-6x\\\implies 9x+6x= 54-9\\\implies 15x = 45\\\\\implies x = \dfrac{45}{15} \\\\\implies x = 3$

$\implies y = 6$

$\boxed{\boxed{\bold{Therefore, \ the \ number \ is \ 36.}}}}}$

                                                       

Answer 2

Question :

The sum of the digit of two number is 9 the number is 6 times the units digit. find the number .

Solution :

Let the digits at units place and tens place of the given number be x and y .

⇒Number = 10y+x

According to the Question:

The sum of the digits is 9

⇒x + y = 9

⇒y = 9 - x....(1)

and,the number is 6 times the units

⇒10y + x = 6x....(2)

Now solve two equations

put y=9-x in equation (2)

$\sf \implies10(9 - x) + x = 6x$

$\sf \implies90 - 10x + x = 6x$

$\sf \implies90 - 9x = 6x$

$\sf \implies90 = 15x$

$\sf \implies x = \cancel{\dfrac{90}{15} } = 6$

Now put x = 6 in equation (1)

$\sf \implies y = 9 - 6 = 3$

Therefore,

The number

= 10x + y

= 10(3) + 6

= 36

____________________________

Verification:

1) The sum of the digits is 9

x + y = 9

⇒3+6= 9

2) The number is 6 times the units

10y+ x = 6x

⇒10(3)+6= 6×6

⇒36=36