A cistern, internally measuring 150 cm × 120 cm × 100 cm, has 129600 \(cm^3\) 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 ocerflowing 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

\(= \ \frac{n}{17} \ × \ 22.5 \ × \ 7.5 \ × \ 6.5 \)

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

\(\Rightarrow n × 22.5 × 7.5 × 6.5 = 1850400 + \frac{n}{17} × (22.5 × 7.5 × 6.5) \)

Solving this we get,

n = 1792.41

Therefore, 1792 bricks were placed in the cistern.