A cistern

Given
Volume of cistern = {tex}150 \times 120 \times 110 \mathrm { cm } ^ { 3 } = 1980000 \mathrm { cm } ^ { 3 }{/tex}
Volume of water = 129600 cm³
Volume of one brick = {tex}22.5 \times 7.5 \times 6.5 \mathrm { cm } ^ { 3 } = 1096.875 \mathrm { cm } ^ { 3 }{/tex}

Each brick absorbs one - seventeenth of its volume of water
Volume of water absorbed by one brick =    {tex}\frac { 1 } { 17 } \times{/tex} volume of brick

      =  {tex}\frac { 1 } { 17 } \times 1096.875 \mathrm { cm } ^ { 3 }{/tex}

     = 64.52 cm³
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 = {tex}n \times \frac { 1 } { 17 } \times 1096.875 \mathrm { cm } ^ { 3 }{/tex}
{tex}\therefore{/tex} Volume of water left in cistern = {tex}= \left( 129600 - \frac { n } { 17 } \times 1096.875 \right) \mathrm { cm } ^ { 3 }{/tex}
Since the cistern is filled upto the brim.

Therefore, Volume of the cistern  = Volume of water left in the cistern + Volume of bricks 
{tex} 1980000{/tex}  = {tex}129600 - \frac { n } { 17 } \times 1096.875 + n \times 1096.875 {/tex}
{tex}n \times 1096.875 - \frac { n } { 17 } \times 1096.875 = 1980000 - 129600{/tex}
{tex}1096.875 \times \left( n - \frac { n } { 17 } \right) = 1850400{/tex}
{tex}1096.875 \times \frac { 16 n } { 17 } = 1850400{/tex}
{tex}17550 \times \frac { n } { 17 } = 1850400 \Rightarrow n = \frac { 1850400 \times 17 } { 17550 } = 1792.41 {/tex}

since the number of bricks cannot be in decimals

therefore, required number of bricks = 1792