# 3. A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm3 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 overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?

The total volume of the cistern is :      $=\ 150\times 120\times 110\ =\ 1980000\ cm^3$

And the volume to be filled in it is  $= 1980000 - 129600\ =\ 1850400\ cm^3$

Now let the number of bricks be n.

Then the volume of bricks    :   $= n\times 22.5\times 7.5\times 6.5 \ =\ 1096.87n\ cm^3$

Further, it is given that brick absorbs one-seventeenth of its own volume of water.

Thus water absorbed  :

$=\ \frac{1}{17}\times 1096.87n\ cm^3$

Hence we write :

$1850400\ +\ \frac{1}{17}( 1096.87n)\ =\ 1096.87n$

$n\ =\ 1792.41$

Thus the total number of bricks is 1792.

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