Question 16

A two digit number is such that the product of its digits is 12. When 36 is added to this number the digits are interchanged. Find the numbers.

Solution:

Let "x y" be the required two digit number

A two digit number such that the product of its digits is 12

x(y) = 12

y = 12/x  ---- (1)

When 36 is added to the number the digits are interchanged

x y + 36 = y x

10 x + y + 36 = 10 y + x

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

9 x - 9 y = -36

Now we are going to divide the whole equation by 9,so we get

x - y = -4  --- (2)

Now we are going to apply the value of y that is first equation in the second equation.

x - (12/x) = -4

x² - 12  = - 4 x

x² + 4 x - 12 = 0

x² + 6 x - 2 x - 12 = 0

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

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

x - 2 = 0             x + 6 = 0

x = 2                     x = -6

To get the value of y we have to apply 2 instead of x in the first equation

y = 12/x

y = 12/2

y = 6

Therefore the required two digit number is 26

Verification:

A two digit number such that the product of its digits is 12

2 (6) = 12

12 = 12

When 36 is added from the number the digits are interchanged

26 + 36 = 62

62 = 62 