Question

A two digit number is 4 times the sum of its digits and twice the product of its digits.Find the number.

Answer 1

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 become
1y
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:

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)