In 80 litres pure milk, 8 litres of milk is replaced by water if this process…
2024
In 80 litres pure milk, 8 litres of milk is replaced by water if this process is repeated two times then what will be the ratio of milk and water in the final mixture?
- A.
81 ∶ 19
- B.
19 ∶ 81
- C.
63 ∶ 17
- D.
17 ∶ 63
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Correct answer: A
Given: Initial quantity of pure milk = 80 litres. Each time 8 litres of mixture is removed and replaced by water. The process is repeated two times.
Idea: When x litres are removed from a total of V litres, the fraction of milk remaining after one replacement is (1 - x/V). Repeating the process n times multiplies this fraction n times.
Fraction of milk remaining after one replacement = 1 - 8/80 = 1 - 0.1 = 0.9 = 9/10.
After two repetitions the fraction = (9/10)^2 = 81/100.
Amount of milk = 80 × 81/100 = 64.8 litres.
Amount of water = 80 - 64.8 = 15.2 litres.
Ratio milk:water = 64.8 : 15.2 = (64.8 ÷ 0.8) : (15.2 ÷ 0.8) = 81 : 19.
Answer: 81 : 19