Correct Answer - Option 5 : None of these
Given:
Initially milk : water is 3 : 2
15 liters of mixture is taken and replaced by the milk,
Then the ratio is 3 : 1
Calculation:
Initially milk : water = 3 : 2,
Total units of mixture = 3 + 2 = 5 units
Out of 5 units,
⇒ Milk = 3/5 and Water = 2/5
Let the total mixture be 5x,
Then milk will be 3x/5 and water will be 2x/5
Now 15 liters of mixture is taken,
In that 15 liters,
⇒ milk = 3/5 × 15 = 9 liters and water = 2/5 × 15 = 6 liters
Now the proportion of Milk and Water,
⇒ Milk/Water = 3x – 9/2x – 6
Now 15 liters of mixture is replaced by milk,
⇒ Milk/Water = 3x – 9 + 15/2x – 6
⇒ Milk/Water = 3x + 6/2x – 6
According to the question,
⇒ 3x + 6/2x – 6 = 3/1
⇒ 3x + 6 = 3 (2x – 6)
⇒ 3x + 6 = 6x – 18
⇒ 3x = 24
⇒ x = 24/3 = 8
Total quantity of a mixture,
⇒ 5 × 8 = 40 liters
∴ The total quantity of a mixture is 40 liters.