The ratio of alcohol and water in vessels A and B are 3:7 and 4:11, respectively...

Given : The ratio of alcohol and water in vessels A and B are 3:7 and 4:11, respectively.

5 litres and 7 litres solutions from vessels A and B. respectively are mixed in vessel C.

To Find : Ratio of water and alcohol in the solution in C?

Solution:

The ratio of alcohol and water in vessels A = 3 : 7

Solution Taken = 5 litre

=> Alcohol = ( 3/10) * 5 = 1.5 litre

Water = 5 - 1.5 = 3.5 litre

The ratio of alcohol and water in vessels B = 4 : 11

Solution Taken = 7 litre

=> Alcohol = ( 4/15) *7 = 28/15 litre

Water = ( 11/15) *7 = 77/15 litre

Total water = 3.5 + 77/15 = 7/2 + 77/15

= ( 105 + 154) /30

= ( 259)/30

Total alcohol = 1.5 + 28/15 = 3/2 + 28/15

= ( 101) / 30

ratio of water and alcohol in the solution in C

( 259)/30 : ( 101) / 30

= 259 : 101

ratio of water and alcohol in the solution in C = 259 : 101

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