Question

A two digit number is such that the product of its digits is 16. If 54 is subtracted from the number, the digits are interchanged. Find the number.

Answer 1

Let the two-digit number have tens digit = x and units digit = y.

Product of digits is 16:

xy = 16

Original number = 10x + y:

After subtracting 54, digits are interchanged:

10x + y − 54 = 10y + x

9x − 9y = 54

x − y = 6

xy = 16

x − y = 6

From x − y = 6,

x = y + 6

Substitute in xy = 16:

(y + 6)y = 16

y² + 6y − 16 = 0

(y + 8) (y − 2) = 0

y = 2 or y = −8

x = y + 6 = 8

The two-digit number is:

82