Three containers X, Y and Z have capacities of 10, 20 and 30 litres respectively. X, which is empty is filled with water from Y. Y is then filled with the wine from Z. X is now emptied into Z. The entire operation is repeated. What would be the strength of wine in the container Z?

Operations

Containers X (Water: Wine)

Container Y (Water: Wine)

Containers Z (Water: Wine)

Initially

0

Water = 20

30 (Wine)

X is completely filled by Y

Water = 10

Water = 10

30

Y is completely filled by Z

Water = 10

Water = 10

Wine = 10

20

X is poured into Z

0

Water = 10

Wine = 10

10: 20

X is completely filled by Y

Water = 5

Wine = 5

Water = 5

Wine = 5

10: 20

Y is completely filled by Z

Water = 5

Wine = 5

Water= 5 + $$\frac{10}{3} = \frac{25}{3}$$
Wine = 5 + $$\frac{20}{3} = \frac{35}{3}$$

Water= 10 - $$\frac{10}{3} = \frac{20}{3}$$
Wine = 20 - $$\frac{20}{3} = \frac{40}{3}$$

X is poured into Z

0

Water = $$\frac{25}{3}$$
Wine = $$\frac{235}{3}$$

Water = $$\frac{20}{3} + 5 = \frac{35}{3}$$
Wine = $$\frac{40}{3} + 5 = \frac{55}{3}$$