Question

A two-digit number is 4 times that the sum of its digits and twice the product of its digits . find the number​

Answer 1

Answer:

two methods

1st method

Step-by-step explanation:

two digits, x & y

10x + y = the number

:

A two digit number is 4 times the sum of its digits

10x + y = 4(x+y)

10x + y = 4x + 4y

10x - 4x = 4y - y

6x = 3y

divide both sides by 3

2x = y

" and twice the product of its digit."

10x + y = 2xy

Replace y with 2x

10x + 2x = 2*x*2x

12x = 4x^2

Divide both sides by 4x

3 = x

then

y = 2(3)

y = 6

:

the number = 36

:

You can confirm this in both statement:

36 = 4(3+6)

and

36 = 2(3*6)

2nd method

Sol:

let the digits be x and y

let x is in the tens place then

it sill become 10x let y is in once place the it will become1y

the original number be 10x+y

from the question

10x+y=4(x+y)

10x+y=4x+4y

10x-4x+y-4y=0

6x-3y=0

2x-y=0

2x=y. eq-1

again according to question

10x+y=2(xy)

substitute y=2x

10x+2x=2x(2x)

12x/2x=2x

6=2x

x=3

if x=3 then y=?

2x=y

y=6

the number is 36

Answer 2

AnswEr :

36

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

A two - digit number is 4 times that the sum of it's digit and twice the product of its digit.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The number.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the digit at ten's place be r

Let the digit at one's place be m

The original number = 10r + m

$\bf{\underline{\underline{\bf{According\:to\:the\:question\::}}}}}$

→ 10r + m = 4(r+m)

→ 10r + m = 4r + 4m

→ 10r - 4r =4m-m

→ 6r = 3m

→ 2r = m................(1)

Now,

→ 10r + m = 2rm

Putting the value of m in above using,we get;

→ 10r + 2r = 2× r × 2r

→ 12r = 4r²

→ 4r² - 12r = 0

→ 4r(r-3)=0

→ r-3 = 0/4r

→ r - 3 = 0

→ r = 3

Putting the value of r in equation (1), we get;

→ m = 2 × 3

→ m = 6

Thus;

The number =10r + m = 10(3) + 6 = 30+6 = 36.