A solution of 72 litres contains alcohol and spirit in the ratio 8: x. if 24 litres of spirit is added to the solution, the ratio becomes 1:1. find the value of x.
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Total solution = 72 litres
Sum of the ratios = x + 8
Amount of :
Alcohol = 8/(x + 8) × 72 = 576/(x + 8)
Spirit = x/(x + 8) × 72 = 72x / (x + 8)
If we add 24 litres of spirit we have :
72x/(x + 8) + 24
The new ratio is :
{576/(x + 8)} / {72x/(x + 8) + 24)} = 1/1
576/(x + 8) = 72x/(x + 8) + 24
Multiplying through by (x + 8)
576 = 72x + 24(x + 8)
576 = 72x + 24x + 192
576 - 192 = 96x
384 = 96x
x = 384/96
x = 4
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