Question

A vessel is filled with a mixture of spirit and water, 70% of which is spirit.After 9litres are taken out and the vessel is filled water, there remains 58 1/3% of spirit; find the contents of the vessel.

Answer 1

let x be the mixture of 0.7x spirit + 0.3x water
remaining after 9 L is (x-9), mixture of 0.7(x-9) spirit + 0.3(x-9) water
after added 9 L of water, 
mixture of  0.7(x-9) spirit + 0.3(x-9)+9 water
0.7(x-9)/x=175/(3*100)
solving for x,
x=54L
initially 37.8L Spirit + 16.2L water
finally 31.5L Spirit + 22.5L water