Question

A two-digit number is such that the product of digit is 12. When 36 is added to the number the digits interchange their places. Determine the number.

Answer 1

SOLUTION:

Let the two digit number be 10x + y

Given : product of its digits(xy) = 12

xy = 12...................(1)

When 36 is added to the number, the digits interchange their places

10x + y + 36 = 10y + x

10x + y - 10y - x = - 36

9x - 9y = - 36

9(x - y) = - 36

x - y = - 36/9

x - y = - 4

x = - 4 + y……………….(2)

Put this value of x in eq 1.

xy = 12

(- 4 + y)y = 12

-4y + y² = 12

y² - 4y - 12 = 0

y² - 6y + 2y - 12 = 0

[By middle term splitting]

y(y - 6) + 2(y - 6) = 0

(y - 6 ) ( y + 2) = 0

(y - 6 ) = 0   or ( y + 2) = 0

y = 6  or y = - 2

Since, a digit can't be negative, so y ≠ - 2.

Therefore , y = 6

Put this value of y in eq 1,

xy =12

x× 6 = 12

x = 12/6 = 2

x = 2

Required number = 10x + y  

= 10(2) + 6

= 20 + 6

Required number = 26

Hence, the Required two digit number is 26.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hlo

here is ur solution..

let the number be 10x + y

A.T.Q..
xy = 12 ...... ( i )

then ,
10x + y + 36 = 10y + x

10x - x + y - 10y = 36

9x - 9y = 36

x - y = 4

x = y + 4. ( putting this value in equation 1 )

____

y ( y + 4 ) = 12

y² + 4y = 12

making quadric equation

y² + 4y - 12 = 0
solving this

( y - 6 ) ( y + 2 ) = 0

so , y = 6 or - 2

since value cann't be negative

xy = 12

x × 6 = 12

x = 12 / 6

x = 2

no. will be = 10x + y

10 × 2 + 6

20 + 6

26✔✔

hope it helps