Question

The milk and water. In two vessels a and b are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c containing half milk and half water

Answer 1

if the a vessel contains half milk and half water
and the b vessel also contain half milk and half water
then the mixture in vessel c will contain half milk and half water.

Answer 2

SOLUTION:-

Vessel A :

[4:3 ⇒ 4+3  =  7,   M⇒4/7,   W⇒ 3/7]

Let "x" be the quantity of mixture taken from vessel A to obtain a new mixture in vessel C.  

Quantity of milk in "x"  =  (4/7)x  =  4x/7

Quantity of water in "x"  =  (3/7)x  =  3x/7

Vessel B :

[ 2:3 ⇒ 2+3 = 5,   M⇒ 2/5,   W⇒ 3/5 ]

Let "y" be the quantity of mixture taken from vessel B to obtain a new mixture in vessel C.  

Quantity of milk in "y"  =  (2/5)y  =  2y/5

Quantity of water in "y"  =  (3/5)y  =  3y/5

Vessel A and B: 

Quantity of milk from A and B is

=  (4x/7) + (2y/5)

=  (20x + 14y) / 35

Quantity of water from A and B is

=  (3x/7) + (3y/5)

=  (15x + 21y) / 35

According to the question, vessel C must consist half of the milk and half of the water. 

That is, in vessel C, quantity of milk and water must be same. 

Therefore,

Quantity of milk in (A+B)  =  Quantity of water in (A+B)

 (20x+14y) / 35  =  (15x+21y) / 35

20x + 14y  =  15x+21y

5x  =  7y

x/y  =  7/5

x : y  =  7 : 5

Hence, the required ratio is 7 : 5.