InterviewSolution
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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 |
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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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