3. A cistern, internally measuring 150 cm × 120 cm × 100 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 being 22.5 cm × 7.5 cm × 6.5 cm?

Given that the dimension of the cistern = 150 × 120 × 110 So, volume = 1980000 cm3 Volume to be filled in cistern = 1980000 – 129600 = 1850400 cm3 Now, let the number of bricks placed be “n” So, volume of n bricks will be = n×22.5×7.5×6.5 Now as each brick absorbs one-seventeenth of its volume, the volume will be = n/(17)×(22.5×7.5×6.5) For the condition given in the question, The volume of n bricks has to be equal to volume absorbed by n bricks + Volume to be filled in cistern Or, n×22.5×7.5×6.5 = 1850400+n/(17)×(22.5×7.5×6.5) Solving this we get, n = 1792.41