Two identical bottles and a jug each carry a scale that starts at 0 at the bottom. Each bottle's top mark is labelled 300 ml with six equal gaps below it. The jug's top mark is labelled 1 ℓ 200 ml with eight equal gaps below it. None of the other marks is labelled. The water in the first bottle stands at the fifth mark above the bottom, the water in the second bottle at the second mark, and the water in the jug at the third mark. (a) Find the volume of water in the jug at first. (b) All the water in the two bottles is poured into the jug, without any spilling. How much water is in the jug in the end? Give your answer in litres.
- conversion fact = unit relation for 1 ℓ = 1000 ml = 1000 cm³
- conversion fact = unit relation for 1 ℓ 200 ml = 1200 ml
- one gap on a bottle = 300 ÷ 6 = 50
- first bottle = 50 × 5 = 250
- second bottle = 50 × 2 = 100
- one gap on the jug = 1200 ÷ 8 = 150
- jug at first = 150 × 3 = 450
- total = 250 + 100 + 450 = 800
- final water volume in litres = converted value of 800 ml = 0.8 ℓ
The answer is 0.8 ℓ.