Question

A two -digit number is seven times the sum of its digits and is also equal to 12 less than three times the product of its digits. Find the number.

Answer 1

84

Explanation:

Let's say that the two digit number is xy.

Here's what we know:

(x+y)*7=xy

x*y*3-12=xy

Since this is a multiple of 7, this can be either:

-14

-21

-28

-35

-42

and so on.

Using guess and check, this can be 84.

Answer 2

84

Explanation:

let the digit at unit place=x

and at ten's place=y

number =10y+x

10y+x=7(x+y)

10y+x=7y+7x

10y-7y=7x-x

3y=6x

y=2x

again

10y+x=3xy-12

10(2x)+x=3x(2x)-12

21 x=6x²-12

6x²-21x-12=0

2x²-7x-4=0

2x²-8x+x-4=0

2x(x-4)+1(x-4)=0

(x-4)(2x+1)=0

x=4,(-1/2 ,rejected)

y=2×4=8

number=10×8+4=84