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

	Scenario 1		Scenario 2
Tank type	Tank J	Tank K	Tank J	Tank K
Volume of the tank	5 u	7 u - 7	5 p	3 p x 2 = 6 p

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

5 u = 5 p --- (1)
7 u - 7 = 6 p
7 u = 6 p + 7 --- (2)

Make u the same.

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

(2) x 5
35 u = 30 p + 35 --- (4)

(3) = (4)
35 p = 30 p + 35
35 p - 30 p = 35
5 p = 35
1 p = 35 ÷ 5 = 7

Volume of Tank K
= 6 p
= 6 x 7
= 42 ℓ

Answer(s): 42 ℓ