**Problem 1:** Two vessels of 48 lit and 42 lit are filled with a mixture of milk and water, the proportion of two vessels being respectively 13:7 and 18:17. if the contents of two vessels are mixed and 20 lit of water be added to the whole what will be the proportion of milk and water in the resulting mixture?

Solution:

M=

w=

264 : 286

132 : 143

12 : 13

**Problem 2:** A vessel contains some liter of pure milk. if 25 lit of water is added to the vessel then ratio of milk and water becomes 12 : 5. 17 liters of mixture is drawn from the vessel and 10 lit of water is added to the mixture. Find the new ratio between milk and water?

Solution:

Milk Water

12 : 5

5——->25

12——>?

in 17 liters 12 liters are milk and 5 liters are water is drawn

Milk=60-12=48

Water=25-5=20

and 10 liters of water is added so 20+10=30

48 : 30

8:5

**Problem 3:** 18 lit of pure water was added to the vessel contains 80 lit of pure milk. 49 lit of the resultant mixture was then sold and some more quantity of pure milk and water was added to the vessel in the ratio of 2:1. if the resultant ratio of Milk and water in the vessel was 4:1 what was the quantity of pure milk added in the vessel?

Solution:

W M

18 + 80——>98 lit

9 : 40

49 lit of mixture was sold out

98-49=49 lit

Some more quantity of pure milk and water was added to the vessel in the ratio of 2:1

Milk=

Water=49-40=9

40+2x=36+4x

2x=4

x=2

**Problem 4:** A vessel contains a mixture of milk and water in the ratio 14:3. 25.5 lit of mixture is taken out from the vessel and 2.5 lit of pure water and 5 lit of milk is added to the mixture. If the resultant mixture contains 20% water. What was the initial quantity of mixture in the vessel before the replacement?

Solution:

Milk Water

14x : 3x

14x+3x = 17x

Milk =

Water = 25.5-21 = 4.5

14x-21+5=12x-1.8+2.5

x=4

17x=17*4=68