Lilian has 2 containers. Container P and Container Q are of different capacities. If Container P is filled by a tap at a rate of 4 litres per minute and Container Q is filled by a tap at a rate of 7 litres per minute, when Container P is completely filled, 5 litres of water flowed out from Container Q. If Container P is filled by a tap at a rate of 6 litres per minute and Container Q is filled by a tap at a rate of 4 litres per minute, when Container P is completely filled, Container Q is only half-filled. What is the capacity of Container Q? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container P	Container Q	Container P	Container Q
Volume of the container	4 u	7 u - 5	6 p	4 p x 2 = 8 p

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

4 u = 6 p --- (1)
7 u - 5 = 8 p
7 u = 8 p + 5 --- (2)

Make u the same.

(1) x 7
28 u = 42 p --- (3)

(2) x 4
28 u = 32 p + 20 --- (4)

(3) = (4)
42 p = 32 p + 20
42 p - 32 p = 20
10 p = 20
1 p = 20 ÷ 10 = 2

Volume of Container Q
= 8 p
= 8 x 2
= 16 ℓ

Answer(s): 16 ℓ