Question

A number is such that the product of its digit is 12. When 36 is added to the number, the digits get reversed. What is the number

Answer 1

let the digits are x and y
so xy=12
10x+y+36=10y+x
9y-9x=36
9(y-x)=36,
y-x=4 =>y=x+4
so x(x+4)=12
${x}^{2} + 4x - 12 = 0 \\ {x}^{2} + 6x - 2x- 12 = 0 \\ x(x + 6) - 2(x + 6) = 0 \\ (x - 2)(x + 6) = 0 \\ so \: x = 2 \: because \: x = - 6 \: is \: not \: possible$
so y=x+4=6
so no.is 26.
I HOPE IT WILL HELP YOU.

Answer 2

Hey there !!

→ Let the ten's digit be x.

And, the unit's digit be y.

A/Q,

→ xy = 12......(1).

→ Original number = 10x + y.

→ And, the number on obtained on reversing the digits = 10y + x .

A/Q,

⇒ 10x + y + 36 = 10y + x.

⇒ 10x - x + y - 10y = - 36.

⇒ 9x - 9y = -36.

⇒ 9( x - y ) = -36.

⇒ x - y = -4.

⇒ y = x + 4.

Put the valu of y in equation (1), we get

⇒ x ( x + 4 ) = 12.

⇒ x² + 4x  - 12 = 0.

⇒ x² 6x - 2x - 12 = 0.

⇒ x ( x + 6 ) - 2 ( x + 6 ) = 0.

⇒ ( x - 2 ) ( x + 6 ) = 0.

⇒ x - 2 = 0.     |   x + 6 = 0.

⇒ x = 2   |  x = -6.

Hence, negative case is not possible , So, x = 2.

So, y = x + 4 = 2 + 4 = 6.

Therefore, the otiginal number = 10x + y.

= 10 × 2 + 6

= 20 + 6.

= 26.

Hence, it is solved.

THANKS

#BeBrainly.