Violet has 2 containers. Container Y and Container Z are of different capacities. If Container Y is filled by a tap at a rate of 3 litres per minute and Container Z is filled by a tap at a rate of 5 litres per minute, when Container Y is completely filled, 5 litres of water flowed out from Container Z. If Container Y is filled by a tap at a rate of 4 litres per minute and Container Z is filled by a tap at a rate of 2 litres per minute, when Container Y is completely filled, Container Z is only one-third-filled. What is the capacity of Container Z? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container Y	Container Z	Container Y	Container Z
Volume of the container	3 u	5 u - 5	4 p	2 p x 3 = 6 p

Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.

3 u = 4 p --- (1)
5 u - 5 = 6 p
5 u = 6 p + 5 --- (2)

Make u the same.

(1) x 5
15 u = 20 p --- (3)

(2) x 3
15 u = 18 p + 15 --- (4)

(3) = (4)
20 p = 18 p + 15
20 p - 18 p = 15
2 p = 15
1 p = 15 ÷ 2 = 7.5

Volume of Container Z
= 6 p
= 6 x 7.5
= 45 ℓ

Answer(s): 45 ℓ