Grace has 2 tanks. Tank Z and Tank A are of different capacities. If Tank Z is filled by a tap at a rate of 4 litres per minute and Tank A is filled by a tap at a rate of 6 litres per minute, when Tank Z is completely filled, 6 litres of water flowed out from Tank A. If Tank Z is filled by a tap at a rate of 4 litres per minute and Tank A is filled by a tap at a rate of 2 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	4 u	6 u - 6	4 p	2 p x 2 = 4 p

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

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

Make u the same.

(1) x 3
12 u = 12 p --- (3)

(2) x 2
12 u = 8 p + 12 --- (4)

(3) = (4)
12 p = 8 p + 12
12 p - 8 p = 12
4 p = 12
1 p = 12 ÷ 4 = 3

Volume of Tank A
= 4 p
= 4 x 3
= 12 ℓ

Answer(s): 12 ℓ