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.
Answers
Answered by
4
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
Answered by
61
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.
Similar questions