Numerical answer
A vessel contains 60 litres of pure milk. 12 litres are drawn out and replaced with water. This operation is performed two more times (three times in all). How many litres of milk are left in the vessel? (Enter the value correct to two decimal places.)
Show answer and solution
Answer: 30.72
Each operation removes 12/60 = 1/5 of whatever is in the vessel, so the milk is multiplied by 4/5 each time while the volume stays 60 L.
Milk left = 60 × (4/5)³ = 60 × 64/125 = 30.72 litres.
Tip: repeated-replacement formula — final = initial × (1 − x/V)ⁿ, where x is the quantity replaced each time and V the vessel volume.
Milk left = 60 × (4/5)³ = 60 × 64/125 = 30.72 litres.
Tip: repeated-replacement formula — final = initial × (1 − x/V)ⁿ, where x is the quantity replaced each time and V the vessel volume.
Saved on this device. Sign in or create a free account to keep it on every device.