Luke has 2 tanks. Tank D and Tank E are of different capacities. If Tank D is filled by a tap at a rate of 3 litres per minute and Tank E is filled by a tap at a rate of 7 litres per minute, when Tank D is completely filled, 5 litres of water flowed out from Tank E. If Tank D is filled by a tap at a rate of 3 litres per minute and Tank E is filled by a tap at a rate of 2 litres per minute, when Tank D is completely filled, Tank E is only one-third-filled. What is the capacity of Tank E? Express your answer in litres.

	Scenario 1		Scenario 2
Tank type	Tank D	Tank E	Tank D	Tank E
Volume of the tank	3 u	7 u - 5	3 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 = 3 p --- (1)
7 u - 5 = 6 p
7 u = 6 p + 5 --- (2)

Make u the same.

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

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

(3) = (4)
21 p = 18 p + 15
21 p - 18 p = 15
3 p = 15
1 p = 15 ÷ 3 = 5

Volume of Tank E
= 6 p
= 6 x 5
= 30 ℓ

Answer(s): 30 ℓ