1Let the total volume of the casket be x.
1st removal and then additon of water:
Amount of wine left = x-9
Amount of water left = 9
Fraction of wine left = x-9x
Fraction of water left=9x
2nd removal:
Now, assuming that the wine and the water mix completely,
Amount of wine removed = (x-9)- x-9x.9
= (x-9)2x
Amount of water removed = 9x- 9x.9
=9.x-9x
2nd addition of water:
Amount of water left = 9.x-9x + 9 = 9x(2x-9)
Hence we have from the question,
(x-9)2x9(2x-9)x = 169
Solving, the possible answer is 45..
