Question

A two digit number is such that the product of its digit is 14. If 45 is added to the number, the digit interchange their place. Find the number?

Answer 1

the nmbr is 27
product of 2 and 7 is 14
when we add 45 to it then it becomes 72

Answer 2

Hi.

Good Question...Keep Progressing...

Here is your answer---

Let the once digit in a number be y and tens digit be x
Thus, Number = 10x +y

According to the Question,
     x * y = 14 --------------------------------------------eq(i) 
 Also,
         10x +y +45 = 10y+x    {As per as question}
           10x - x +y - 10y = -45
             9x - 9y = -45
               9(x - y) = -45
 Thus,       x - y = -5 
                 y =  x + 5 ----------------------------------eq(2)

Putting eq(2) in the eq(1)
 We get, 
    x * y = 14
   x * (x +5) = 14
   x ^2 + 5x = 14
    x^2 +5x - 14 = 0
Splitting the middle term,
  x^2 + 7x - 2x - 14 = 0 
  x( x - 7) - 2( x -7) = 0
    (x - 7)(x - 2) = 0
By Zero Product Rule,
   x - 7 = 0                                       x - 2 = 0
    x = 7                                               x = 2
For, x = 7 in eq(i)
 7 * y =14
     y = 2

For, x = 2 in eq(i)
  2 * y =14
   y = 7

Thus, when x is 7 and y is 2,
  Number = 10x + y
                = 10(7) + 2
                = 70 +2
                = 72
Also, when x is 2 and y is 7,
    Number = 10x + y
                  = 10(2) + 7
                  =  20 + 7
                  = 27

Thus, two digits number will be 72 or 27.

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