Question

9 litre spirit is drawn from a vessel full of



sprit and is then filled with water, this



operation is performed one more times.



the ratio of the quantity of spirit now left



in cask to that of the water is 16:9.Find



the capacity of vessel.

Answer 1

The initial amount of spirit in vessel was 45 liters.

Step-by-step explanation:

Let the vessel contains the amount of spirit = x liters

the amount of spirit is drawn from the vessel = 9 liters

this process is performed by 2 times.

$\text{initial quantity}(1-\frac{\text{amount taken out}}{\text{initial quantity}})^n$

n = number of operation (2)

amount of spirit left  $=[x(1-\frac{9}{x} )^2]$

The ratio of quantity of spirit and water now = 16 : 9

so the equation would be :

$[\frac{x(1-\frac{9}{x})^2 }{x} ]=\frac{16}{(16+9)}$

$(\frac{x-9}{x})^2=\frac{16}{25}$

$(\frac{x-9}{x})=\sqrt{\frac{16}{25} }$

$\frac{x-9}{x}=\frac{4}{5}$

5x - 45 = 4x

5x - 4x = 45

x = 45

The initial amount of spirit in vessel was 45 liters.

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