Ali has $300. He lost 1/3 of it and ends up with $200. To have the $300 again, he needs to win $100 which is ½ of the $200. 1/3 is known as the Losing Fraction (LF) and ½ is known as the Winning Fraction (WF). ½ times 1/3 = 1/6. 1/6 is the product of the LF and WF, known as the PLW. Find the LF and the WF if the PLW is 81/400.

81 = 81 x 1
= 27 x 3
= 9 x 9
**(a and c)**
400 = 400 x 1
= 200 x 2
= 100 x 4
= 80 x 5
= 50 x 8
= 40 x 10
= 25 x 16
**(b and d)**
LF = a/b
WF = c/d
a/b = c/d (1 - a/b)
a d = c (b - a)
Using the above factors, trial and error,
a = 9, b = 25, c = 9 and =16
LF = 9/25 and WF = 9/16