Question
Download Solution PDF40 litres of a mixture contains milk and water in the ratio of 17 : 3. After the addition of some more milk it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Mixture volume = 40 litres
Initial milk to water ratio = 17:3
Final milk to water ratio = 7:1
Formula used:
Initial milk volume = Total volume × Milk ratio / (Milk ratio + Water ratio)
Initial water volume = Total volume × Water ratio / (Milk ratio + Water ratio)
Calculation:
Initial milk volume = 40 × 17 / (17 + 3)
⇒ Initial milk volume = 40 × 17 / 20
⇒ Initial milk volume = 34 litres
Initial water volume = 40 × 3 / (17 + 3)
⇒ Initial water volume = 40 × 3 / 20
⇒ Initial water volume = 6 litres
Let the added milk be x litres.
Final milk volume = Initial milk volume + x
Final water volume = Initial water volume
New ratio (milk to water) = (34 + x) / 6 = 7 / 1
⇒ (34 + x) / 6 = 7
⇒ 34 + x = 7 × 6
⇒ 34 + x = 42
⇒ x = 42 - 34
⇒ x = 8 litres
∴ The correct answer is option 1.
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