South African Mathematics Olympiad

Question

When a water-tank is 30% empty it has 30 litres more in it than when it is 30% full. How many litres can the tank hold when it is full?

Accepted Answer

75 If W is the number of litres the tank can hold, then when it is 30% empty it is holding 0.7W litres, and so we have 0.7W = 0.3W + 30, i.e. 0.4W = 30 and then W = 30 0.4 = 300 4 = 75.