1.

4 litres of milk is removed from a 40 litre container of milk and it is then replaced with 4 litres of water. This procedure is repeated two more times. How much milk is now present in the container?1). 29.16 litres2). 28 litres3). 27.36 litres4). 26.34 litres

Answer»

Original quantity of milk in the container = 40 litres

At first, the quantity of liquid removed from the container = 4 litres

Quantity of milk left in the container after first procedure = 40 – 4 = 36 litres

Let us try to write this quantity in terms of 40 litres to make it easier to do bigger calculations.

36 litres = $(40\;\left[ {1 - \FRAC{4}{{40}}} \right])$

Quantity of milk left in the container after SECOND procedure

$(\begin{array}{l} = \left\{ {40\;\left[ {1 - \frac{4}{{40}}} \right]} \right\} - \left\{ {\frac{4}{{40}}of\;40\;\left[ {1 - \frac{4}{{40}}} \right]} \right\}\\ = \left\{ {40\;\left[ {1 - \frac{4}{{40}}} \right]} \right\} \times \left[ {1 - \frac{4}{{40}}} \right]\\ = \left[ {40{{\left( {1 - \frac{4}{{40}}} \right)}^2}} \right]\END{array})$ 

Similarly, quantity of milk left in the container after third procedure

$(\begin{array}{l} = \left[ {40{{\left( {1 - \frac{4}{{40}}} \right)}^3}} \right]\\ = \left[ {40{{\left( {\frac{{40 - 4}}{{40}}} \right)}^3}} \right]\\ = \left[ {40{{\left( {\frac{{36}}{{40}}} \right)}^3}} \right]\\ = \left[ {40{{\left( {\frac{9}{{10}}} \right)}^3}} \right]\\ = \left[ {40 \times \frac{9}{{10}} \times \frac{9}{{10}} \times \frac{9}{{10}}} \right]\end{array})$ 

= 29.16 litres

∴ Milk now present in the container is 29.16 litres



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