Question

a two digit number is such that it is 4 times the sum of the digits it is also equal to 3 times the product of digits .find the number

Answer 1

$\huge{\underline{\bold{Solution :}}}$
$<b><i>$

Let the one's digit be x.

And ten's digit be y.

Original number = 10x + y

Now, it is given that the number is four times the sum of the number, i.e., 4(x + y).

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

=> 10x + y = 4x + 4y

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

=> 6x - 3y = 0

=> 3(2x - y ) = 0

=> 2x - y = 0

=> 2x = y

Also, it is given that it is also equal to 3 times the product of digits, i.e, 10x + y = 3xy.

Since y = 2x and 10x+y = 3xy, we have

So, on substituting the value of y = 2x in

=> 10x + y = 3xy.

=> 10x + 2x = 3x( 2x )

=> 12x = 6x²

=> 12x - 6x² = 0

=> 6x ( 2 - x) = 0

So, x = 0 and x = 2

Since x can't be zero, x = 2

On substituting the value of x in y = 2x.

we get;

y = 2x

=> y = 2 × 2

=> y = 4

So,

Original number = 10x + y

=> 10 × 2 + 4

=> 20 + 4

=> 24


Hence, the number is $\bold{24.}$


Thanks for the question!

Answer 2

here is your answer OK


Let the two-digit number be written as AB, where A is not 0.

We can set up two equations from the given information

10A + B = 4(A+B)
10A + B = 3 * A * B
From 1) 10A + B = 4A + 4B so 6A = 3B and B = 2A

Using this in 2) gives 10A + 2A = 3 * A * 2A

Therefore 12A = 6A^2

rearranging gives 6A^2 - 12A = 0 and this can be written 6A ( A -2) = 0

From this A = 0 or A = 2

To have a two-digit number AB, A cannot be 0.

If A = 2, then B = 4, giving 24 as our two-digit number.

Checking this: 4 * (2+4)= 4 * 6 = 24 and 3 * 2 * 4 = 24