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Question : A 10-litre solution of milk and water contains 8 litres of milk. 2 litres of the solution is replaced by pure milk and mixed. The process is repeated two more times. How much milk (in litres) is present in the mixture so obtained?

Option 1: 8.976

Option 2: 8.597

Option 3: 8.796

Option 4: 8.679


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 8.976


Solution : Given,
A 10-litre solution of milk and water contains 8 litres of milk.
2 litres of the solution is replaced by pure milk and mixed.
Final proportion = Initial proportion$\times(\frac{\text{Volume before replacement}}{\text{Volumne after replacement}})^n$
Where, n = number of times the process is repeated.
Final proportion of water = $\frac{2}{10}\times(\frac{8}{10})^3=\frac{1}{5}\times(\frac{4}{5})^3=\frac{64}{625}$
Now, initial proportion of mixture = $\frac{2}{10}=\frac15$
⇒ Volume before replacement = 10 – 2 = 8 litres
⇒ Volume after replacement = 8 + 2 = 10 litres
⇒ Proportion of milk = $\frac{625-64}{625}=\frac{561}{625}$
⇒ Quantity of milk = $\frac{561}{625}\times 10=8.976$ litres
Hence, the correct answer is 8.976 litres.

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