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
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
= n × 22.5 × 7.5 × 6.5
= 1850400 + n/(17) × (22.5 × 7.5 × 6.5)
Solving this we get,
n = 1792.41