Question 53

# 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?

Solution

Table given shows the operations given:

0

 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 = $$\frac{40}{3} + 5 = \frac{55}{3}$$

Total quantity in container Z = $$\frac{35}{3} + \frac{55}{3} = 30$$

Required percent = $$\frac{\frac{55}{3}}{30} * 100$$ = 61% (Approx)