Question

. A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits
.Find the number

Answer 1

AnswEr :

24

$\bf{\large{\green{\underline{\underline{\bf{Given\::}}}}}}$

A two digit number is four times the sum of the digits. It is also equal to 3 times the products of digits.

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

The number.

$\bf{\large{\orange{\underline{\underline{\bf{Explanation\::}}}}}}$

Let the unit's place be R

Let the ten's place be M

The number = 10R + M

$\bf{\large{\underline{\underline{\tt{\red{A.T.Q\::}}}}}}$

$\longrightarrow\tt{10R + M=4(R+M)}\\\\\\\longrightarrow\tt{10R+M=4R+4M}\\\\\\\longrightarrow\rr{10R-4R=4M-M}\\\\\\\longrightarrow\tt{\cancel{6}R=\cancel{3}M}\\\\\\\longrightarrow\tt{\red{2R=M......................(1)}}$

And;

$\longrightarrow\tt{10R+M=3(RM)}\\\\\\\longrightarrow\tt{10R+2R=3(R)(2R)}\\\\\\\longrightarrow\tt{12R=3\times 2R^{2} }\\\\\\\longrightarrow\tt{12\cancel{R}=6\cancel{R}^{2} }\\\\\\\longrightarrow\tt{12=6R}\\\\\\\longrightarrow\tt{R\:=\:\cancel{\dfrac{12}{6} }}\\\\\\\longrightarrow\tt{\red{R\:=\:2}}$

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

$\longrightarrow\tt{M\:=\:2(2)}\\\\\\\longrightarrow\tt{\red{R\:=\:4}}$

So,

$\bf{The\:number\:is\:10R+M=10(2)+4\:=\:20+4}\\\\\bf{\underline{\pink{The\:number\:is\:24.}}}$

Answer 2

Answer:

Step-by-step explanation:

Given :-

A two digit number is four times the sum of the digits.

It is also equal to 3 times the product of digits.

To Find :-

The Number

Solution :-

Let 10y + x be the two digit number respectively.

⇒ 10y + x = 4 (y + x)

⇒ 10y + x = 4y + 4x

⇒ 10y - 4y = 4x - x

⇒  6y = 3x

⇒ x =  6/3 y

⇒ x = 2y ............(i)

Putting Eq (i) value, we get

⇒ 10y + 2y = 3y(2y)

⇒ 12y = 6y²  

⇒12 = 6y

⇒ y = 2

⇒  x = 2(2)

⇒ x = 4

Number = 10(2) + 4 = 20 + 4 = 24

Hence, The required number is 24.