IMC 2017 Q18
18. A water tank is \(\dfrac{5}{6}\) full. When 30 litres of water are removed from the tank, the tank is \(\dfrac{4}{5}\) full.
How much water does the tank hold when full?
- A 180 litres
- B 360 litres
- C 540 litres
- D 720 litres
- E 900 litres
Intermediate Mathematical Challenge 2017, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 900 litres
Let the capacity of the tank be \(x\) litres. Then \(30 = \frac{5x}{6} - \frac{4x}{5} = \frac{25x - 24x}{30} = \frac{x}{30}\). So \(x = 30 \times 30 = 900\).
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).