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