Liam has 2 tanks. Tank Z and Tank A are of different capacities. If Tank Z is filled by a tap at a rate of 3 litres per minute and Tank A is filled by a tap at a rate of 7 litres per minute, when Tank Z is completely filled, 8 litres of water flowed out from Tank A. If Tank Z is filled by a tap at a rate of 6 litres per minute and Tank A is filled by a tap at a rate of 5 litres per minute, when Tank Z is completely filled, Tank A is only half-filled. What is the capacity of Tank A? Express your answer in litres.

	Scenario 1		Scenario 2
Tank type	Tank Z	Tank A	Tank Z	Tank A
Volume of the tank	3 u	7 u - 8	6 p	5 p x 2 = 10 p

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

3 u = 6 p --- (1)
7 u - 8 = 10 p
7 u = 10 p + 8 --- (2)

Make u the same.

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

(2) x 3
21 u = 30 p + 24 --- (4)

(3) = (4)
42 p = 30 p + 24
42 p - 30 p = 24
12 p = 24
1 p = 24 ÷ 12 = 2

Volume of Tank A
= 10 p
= 10 x 2
= 20 ℓ

Answer(s): 20 ℓ