In a vessel there is 50litre mixture of milk and water and their ratio in the mixture is 3:2 respectively .some quality of water is added to the mixture and the ratio of milk to water becomes 12:13.find the quality of mixture taken out.
Answers
Answer:
Quantity of milk in the mixture = 50 × (3/5) = 30
Quantity of water in the mixture = 50 × (2/5) = 20
Let the quantity of water be added x liters to make ratio equal
According to the question
⇒ (20 + x)/30 = 1/1
⇒ 20 + x = 30
⇒ x = 30 – 20
⇒ x = 10 liters
Step-by-step explanation:
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Let the initial quantity of mixture be x with milk:water = 3:2
Amount of milk in the mixture = 3/5 x and water = 2/5 x
When 25 L of mixture is removed, amount of milk left = 3/5 x - 3/5 * 25 = 3/5 x - 15
Amount of water left = 2/5 x - 2/5 * 25 = 2/5x - 10
Amount of water after 15 more litres of water is added = 2/5x -10+15 = 2/5x + 5
Ratio of milk to water = 3/5x - 15 : 2/5 x + 5 = 3:7
(3/5x - 15)/(2/5 x +5) = 3/7
Cross multiply
21/5 x -105 = 6/5 x + 15
21/5 x - 6/5x = 15 +105
3x = 120
x = 40 L
Initial quantity of mixture = 40 L
Check:
In 40 L of initial mixture, milk = 40*3/5 = 24 L and water = 16 L
Amount of milk left when 25 L of mixture is removed = 24 - 3/5 * 25 = 24 - 15 = 9 L
Amount of water left after 25 lit of mixture is removed = 16 - 2/5 * 25 = 6 L
Amount of water after adding 15 L of water = 6 + 15 = 21L
Milk to water ratio in the new mixture = 9:21 = 3:7