Question

Two vessels contain a mixture of spirit and water. in the first vessel the ratio of spirit to water is 8 : 3 and in the second vessel the ratio is 5 : 1. a 35 litre cask is filled from these vessels so as to contain a mixture of spirit and water in the ratio of 4 : 1. how many litres are taken from the first vessel?

Answer 1

Lets assume 3 containers A,B and C .
Where C has got capacity of 35 Lts.

For container C , ratio of spirit and water = 4:1
Assuming volume of spirit be 4x and that of water be x
then, 4x + x = 5x = 35 litre

x = 7

So spirit in C = 28 litre and water = 7 litre

Similarly in container A let spirit be 8y litre and water to be 3y litre
And that in B let spirit be 5z litre and water be z litre .

Now A/q , total volume of spirit in container C = 8y + 5z = 28   .......(1)
while that of water = 3y + z = 7    ............(2)

Solving (1) and (2) fetches y = 1      and z = 4

So in container A  spirit = 8 litres and water = 3 litres
And in container in B, spirit = 20 litres and water = 4 litres

Therefore volume of container A considered = 8 + 3 = 11 Litres
And that of B = 20+4 = 24 litres

Hope my answer is correct.