There are two vessels containing the mixture of milk and water. In the first vessel the water is 2/3

Ques - There are two vessels containing the mixture of milk and water. In the first vessel the water is 2/3 of the milk and in the second vessel water is just 40% of the milk. In what ratio these are required to mix to make 24 litres mixture in which the ratio of water and milk is 1 : 2?

(a) 4 : 3

(b) 5 : 7

(c) 5 : 2

(d) 7 : 5

Solution -

Let,

First vessel = A

Second vessel = B

The ratio of water to milk in vessel A = 2 : 3

Concentration of water in vessel A = 2/5

Concentration of Milk in vessel A = 3/5

And,

The ratio of water to milk in vessel B = 40%

= 40/100

= 2/5

= 2 : 5

Concentration of water in vessel B = 2/7

Concentration of Milk in vessel B = 5/7

Let us take,

Q1 litres from Vessel A and Q2 litres from vessel B and mix them.

The amount of water in this mixture would be

= (2/5)Q1 + (2/7)Q2 litres

And,

The amount of milk in this mixture would be

= (3/5)Q1 + (5/7)Q2 litres

 The ratio of water to milk in the final mixture would be 1 : 2  (given)

[ (2/5)Q1 + (2/7)Q2 / (3/5)Q1 + (5/7)Q2 ] = 1/2

[ (2/5)Q1 + (2/7)Q2 ] = 1/2 [(3/5)Q1 + (5/7)Q2]

[ (2/5)Q1 + (2/7)Q2 ] = [ (3/10)Q1 + (5/14)Q2]

[ (2/5)Q1 - (3/10)Q1 ] = [ (5/14)Q2 - (2/7)Q2 ]

[ (1/10) Q1 ] = [ (1/14) Q2 ]

Q1/Q2 = 10/14

Q1/Q2 = 5/7

Q1 : Q2 = 5 : 7

Therefore,

The ratio of First mixture to Second mixture = 5 : 7.

Hence, 

The correct answer is option (b) 5 : 7.

Also, this answer can be solved by using alligation.

Thank You