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

	Scenario 1		Scenario 2
Tank type	Tank M	Tank N	Tank M	Tank N
Volume of the tank	4 u	7 u - 6	5 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 = 5 p --- (1)
7 u - 6 = 8 p
7 u = 8 p + 6 --- (2)

Make u the same.

(1) x 7
28 u = 35 p --- (3)

(2) x 4
28 u = 32 p + 24 --- (4)

(3) = (4)
35 p = 32 p + 24
35 p - 32 p = 24
3 p = 24
1 p = 24 ÷ 3 = 8

Volume of Tank N
= 8 p
= 8 x 8
= 64 ℓ

Answer(s): 64 ℓ