Question

2. Vessel A contains milk and Vessel B contains
water. Initially milk in Vessel A and water in
Vessel B is in ratio 2:3. 20% of the volume of the
Vessel A is poured in Vessel B and then half of
the final volume of Vessel B is poured in Vessel
A. The process repeated again.
Find the ratio of water in Vessel A to Vessel B.
1. 3:7
2. 7:3
3. 7:43
4. 43:7

Answer 1

3=7:43 Step-by-step explanation:

Answer 2

Given :   Vessel A contains milk and Vessel B contains water.

Initially milk in Vessel A and water in Vessel B is in ratio 2:3.

20% of the volume of the Vessel A is poured in Vessel B and

then half of the final volume of Vessel B is poured in Vessel A.

The process repeated again.  

To Find : the ratio of water in Vessel A to Vessel B.

1. 3:7

2. 7:3

3. 7:43

4. 43:7

Solution:

milk in Vessel A and water in Vessel B is in ratio 2:3

Milk = 200x

Water = 300x

20% of the volume of the Vessel A is poured in Vessel B

Hence (20/100)200x = 40x

Milk left in Vessel A = 200x - 40x  = 160x

Milk in vessel B = 40x  and Water in vessel B = 300x

Half of  final volume of Vessel B is poured in Vessel A.

After that

Milk in vessel B = 20x  and Water in vessel B = 150x

Milk in Vessel A = 160x + 20 = 180x  Water in Vessel A = 150x

20% of the volume of the Vessel A is poured in Vessel B

(20/100) 180x = 36x milk  and (20/100) 150x  = 30x

Left in Vessel A

Milk =  180x - 36x  = 144x   , water = 150x - 30x  = 120x

in Vessel B

Milk =  20x + 36x = 56x   water  =  150x  + 30x  = 180x

Half of  final volume of Vessel B is poured in Vessel A.

Water Left in Vessel B = 180x/2 = 90x

Water in Vessel A = 120x + 90x = 210x

Ratio

210x : 90x

= 7 : 3

Hence correct option is 2) 7 : 3

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