Andrew has 2 tanks. Tank W and Tank X are of different capacities. If Tank W is filled by a tap at a rate of 3 litres per minute and Tank X is filled by a tap at a rate of 5 litres per minute, when Tank W is completely filled, 6 litres of water flowed out from Tank X. If Tank W is filled by a tap at a rate of 6 litres per minute and Tank X is filled by a tap at a rate of 2 litres per minute, when Tank W is completely filled, Tank X is only one-quarter-filled. What is the capacity of Tank X? Express your answer in litres.

	Scenario 1		Scenario 2
Tank type	Tank W	Tank X	Tank W	Tank X
Volume of the tank	3 u	5 u - 6	6 p	2 p x 4 = 8 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)
5 u - 6 = 8 p
5 u = 8 p + 6 --- (2)

Make u the same.

(1) x 5
15 u = 30 p --- (3)

(2) x 3
15 u = 24 p + 18 --- (4)

(3) = (4)
30 p = 24 p + 18
30 p - 24 p = 18
6 p = 18
1 p = 18 ÷ 6 = 3

Volume of Tank X
= 8 p
= 8 x 3
= 24 ℓ

Answer(s): 24 ℓ