Question

the two digit number is four times the sum and three times the product of its digit .Find the number

Answer 1

Answer:24

Step-by-step explanation:let the two digits be x and y.

Then, the number would be 10x+y (x being in tens place and y in one's place).

According to the quest:-

Case.1-- a two digits number is 4 times the sum of the digits.

= 10x+y=4(x+y)

= 10x-4x=4y-y

= 6x=3y

(÷2) = (2x=y)----- eq.1

According to the quest:-

Case.2-- the number is also equal to 3 times the product of the digits.

10x+y=3xy

Substitute the value of y=2x in place of y.

We get, 10x+2x=(3x)(2x)

= 6x²-12x=0

= 6x(x-2)=0

= 6x=0 so, x=0 or x-2=0 so, x=2.

Consider eq.1:- 2x=y

= 2(2)=y so y=4

OR

= 2(0)=y so y=0

Since we are asked to find out a two digit number. The value of x or y cannot be taking into consideration while its value is 0.

So we take x=2 and y=4

The number:- 10x+y

= 10(2)+4

= 24

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the unit digit and tens digit of the two digit number be x and y respectively.

Number = 10y + x

According to the Question,

⇒ 10y + x = 4(y + x)

⇒ 10y + x = 4y + 4x

⇒ 10y - 4y = 4x - x

⇒ 6y = 3x

⇒ 2y = x  ... (i)

Also, 10y + x = 3xy .... (ii)

⇒ 10y + 2y = 3(2y)y   [From Eq (i)]

⇒ 12y = 6y²

⇒ 6y² - 12y = 0

⇒ 6y(y - 2) = 0

⇒ y = 0, 2

Rejecting y = 0 as tens digit should not be zero for two digit number

⇒ x = 4

Number = 10y + x = 10 × 2 + 4 = 24.

Hence, the required number is 24.