Question

A two digits number is four times the sum of the digits it is also equal to three times product or digits . Find the number

Answer 1

Answer:

Number is 24

Step-by-step explanation:

Let the digit at ten's place be X and unit's place be y.

Also, Let the two digit number be 10x + y.

$according \: to \: condition \: 1 \\ 10x + y = 4(x + y) \\ 10x + y = 4x + 4y \\ 10x - 4x = 4y - y \\ 6x = 3y \\ dividing \: throughout \: by \: 3 \\ 2x = y \\ i.e. \: y = 2x \: \: \: \: - - - (1)$

$according \: to \: condition \: 2 \\ 10x + y = 3xy \: \: \: \: - - - (2) \\ \\ from \: (1) \: and \: (2) \\ 10x + 2x = 3 \times x \times 2x \\ 12x = 6 {x}^{2} \\ div \: throughout \: by \: 6x \\ 2 = x \\ x = 2 \: \: \: \: - - - - (3)$

$since \\ y = 2x \: \: \: \: (from \: 1) \\ y = 2 \times 2 \: \: \: \: (from \: 3) \\ y = 4 \: \: \: \: - - - - (4)$

$the \: original \: number \: \\ = 10x + y \\ = 10 \times 2 + 4 \\ = 20 + 4 \\ = 24$