Question

If two digit number is 4 times the sum of its digit and twice the product of the digits.find the number

Answer 1

Answer.

Let the digit in the ones place be x and tens place be y
Hence the two digit number = 10y + x
Given that the two digit number = 4 times sum of its digits
⇒ 10y + x = 4(x + y)
⇒ 10y + x = 4x + 4y
⇒ 3x – 6y = 0
⇒ 3x = 6y
∴ x = 2y → (1)
It is also given that the two digit number = 2 times product of its digits
⇒ 10y + x = 2xy
Divide by xy both the sides, we get

∴ y = 3
Hence x = 6
The two digit number is (10y + x) = 10(3) + 6 = 36

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the ones place digit be x.

and tens place digit be y.

Number = 10y + x

According to the Question,

⇒ 10y + x = 4(x + y)

⇒ 10y + x = 4x + 4y

⇒ 3x − 6y = 0

⇒ x = 2y .... (i)

⇒ 10y + x = 2xy

Dividing both sides with xy, we get

⇒ 10/x + 1/y = 2

Putting the value of Eq (i), we get

⇒ 10/2y + 1/y = 2

⇒ 5/y + 1/y = 2

⇒ 6/y = 2

⇒ y = 6/2

⇒ y = 3

Putting y's value in Eq (i), we get

⇒ x = 2y

⇒ x = 2(3)

⇒ x = 6

Number = (10y + x) = 10(3) + 6 = 36