Question

A 2-digit number is such that the product of its digit is 8. When 18 is added to the number, the digits interchange their place. Determine the number.​

Answer 1

Let tens digit be X And ones digit be Y

XY = 8

X = 8/Y

Original number = 10X + Y

reversed number = 10Y + X

10X + Y +18 = 10Y + X

9X - 9Y = -18

72/Y - 9Y = -2

9Y^2 -2Y -72

Answer 2

Answer :-

24

Step-By-Step Explanation :-

• Let the digit in the units place = x
• Let the digit in the tens place = y

.°. The number = 10x + y

By interchanging the digits the number becomes 10x + y

By problem (10x + y) - (10y + x) = 18

=> 9x - 9y = 18

=> 9(x - y) = 18

=> x - y = 18/9

=> x - y = 2

=> y = x - 2

(i.e.,) digit in the tens place = x -2

digit in the units place = x

Product of the digits = (x - 2)x

By problem x² - 2x = 8

x² - 2x - 8 = 0

=> x² - 4x + 2x - 8 = 0

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

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

=> x - 4 = 0 or x + 2 = 0

=> x = 4 or x = -2

.°. x = 4 [ °.° x can't be negative ]

.°. The number is 24.