Question

nine litres of solution are drawn from a cask containing water.it is replaced with a similar quantity of pure milk.this operation is done twice.the ratio of water to milk in the cask now is 16:9.how much does the cask hold?

Answer 1

Let there be x litres in the cask.

After n operations,

Water left in vessel / Original quantity = (1 – 9/x)n

16/25 = (1 – 9/x)2

4/5 = 1 – 9/x

∴ x = 45 litres.

Answer 2

Cask hold 45 litters of mixture.

Given:

Nine liters of solution are drawn from a cask containing water.

It is replaced with a similar quantity of pure milk.

This operation is done twice.

The ratio of water to milk in the cask now is 16:9.

Find:

How much does the cask hold?

Formula used:

${(\frac{Water\ left\ in\ vessel}{Original\ quantity})}$ = $(1 - \frac{No\ of\ litter\ removed\ }{x} )^n$

Where  n = No of operations,

             x = initial quantity of water

Explanation:

From above equation:

${(\frac{Water\ left\ in\ vessel}{Original\ quantity})}$ = $(1 - \frac{No\ of\ litter\ removed\ }{x} )^n$

                          $\frac{16}{25}$ =  $(1 - \frac{9 }{x} )^2$

Taking square root of both side,

    $\frac{4}{5}$ =  $(1 - \frac{9 }{x} )$

   $\frac{9}{x}$ = 1 - $\frac{4}{5}$

   $\frac{9}{x}$ = 0.2

  x = 45 litters.

Cask hold 45 litters of mixture.

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