A vessel of capacity 65 litres contains a mixture of

Q: Answer-A vessel of capacity 65 litres contains a mixture of milk and water in an unknown ratio. One-third o...

ATQ, Let initial milk M litres, water W litres. Total volume V M W 65. Each time, 13 of the mixture is removed and replaced with water. Fraction of milk left after one replacement 1 13 23. After two replacements, fraction left 232 49. So final quantity of milk 49M. Final total volume is still 65 L, so final water 65 49M. Given final ratio milk water 16 23 49 M 65 49M 1623 Cross-multiply 23 49M 1665 49M 929M 1040 649M Add 649M both sides 929 649M 1040 1569M 1040 523M 1040 M 1040 352 104052 3 20 3 60 litres. Since total is 65 L W 65 60 5 litres. Answer Initially milk 60 L water 5 L ratio 12 1.

milk and water in an unknown ratio. One-third of the mixture is removed and replaced by pure water. This operation is repeated once more (again removing one-third of the mixture and replacing with water). In the final mixture, the ratio of milk to water is 16 : 23. Find the initial quantities of milk and water in the vessel.

A Initially milk = 30 L; water = 25 L Correct Answer Incorrect Answer

B Initially milk = 60 L; water = 5 L Correct Answer Incorrect Answer

C Initially milk = 40 L; water = 12 L Correct Answer Incorrect Answer

D Initially milk = 20 L; water = 15 L Correct Answer Incorrect Answer

E None of these Correct Answer Incorrect Answer

Solution

ATQ, Let initial milk = M litres, water = W litres. Total volume V = M + W = 65. Each time, 1/3 of the mixture is removed and replaced with water. Fraction of milk left after one replacement = (1 − 1/3) = 2/3. After two replacements, fraction left = (2/3)^2 = 4/9. So final quantity of milk = (4/9)M. Final total volume is still 65 L, so final water = 65 − (4/9)M. Given final ratio milk : water = 16 : 23: (4/9 M) / [65 − (4/9)M] = 16/23 Cross-multiply: 23 × (4/9)M = 16[65 − (4/9)M] (92/9)M = 1040 − (64/9)M Add (64/9)M both sides: (92/9 + 64/9)M = 1040 (156/9)M = 1040 (52/3)M = 1040 ⇒ M = 1040 × (3/52) = 1040/52 × 3 = 20 × 3 = 60 litres. Since total is 65 L: W = 65 − 60 = 5 litres. Answer: Initially milk = 60 L; water = 5 L (ratio 12 : 1).

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