A vessel contains 55% of milk and rest is water and on adding 20 liters of milk it becomes 70% of the total mixture. find mixture
Answers
Find the percentage of water:
100 - 55 = 45%
Find the ratio of milk to water:
milk : water = 55 : 45
Simplify : milk : water = 11 : 9
Find the new percentage:
Percentage of milk = 70%
Percentage of water = 100 - 70 = 30%
Find the new ratio:
milk : water = 70 : 30
Simplify: milk : water = 7 : 3
Make the water ratio the same:
Since the water content did not change, we will make the two water ratio the same:
New ratio milk : water = 7 : 3
Multiply by 3 : New ratio milk : water = 21 : 9
Compare the two ratio and find 1 share:
Old ratio milk : water = 11 : 9
New ratio milk : water = 21 : 9
There is a difference of 21 - 11 = 10 shares
10 shares = 20 litres
1 share = 20 ÷ 10 = 2 litres
Find the new mixture content:
milk = 21 (2) = 42 litres
water = 9 (2) = 18 litres
Answer: The mixture consist of 42 litres of milk and 18 litres of water.
Milk = 3/5 x 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed,
then amount of milk removed = 4/5 x 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
Now 10 lts milk is added => total milk = 18 lts
The required ratio of milk and water in the final mixture obtained
= (8 + 10):2 = 18:2 = 9:1.