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Question

A cistern, internally measuring 150cm×120cm×110cm has 129600cm3 of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one seventeenth of its own volume of water. How many bricks can be put in without the water overflowing, each brick being 22.5cm×7.5cm×6,5cm?

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Solution

We have
volume of cistern =150×120×110cm3=1980000cm3

Volume of water in cister =129600cm3

Volume of one brick =22.5×7.5×6.5cm3=1096.875cm3

volume of water absorbed by one brick =117×1096.875cm3

Let n be the total number of bricks which can be put in the cistern without water overflowing.
then volume of water absorbed by n bricks =n×117×1096.875cm3

Volume of water left in the cistern =(129600n17×1096.875)cm3

Since the cistern is filled upto the brim

volume of water left in the cistern + volume of bricks = volume of the cistern

129600n17×1096.875+n×1096.875=1980000

1096.875×(nn17)=1850400

n=185040017550=1792.411792

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