A cistern, internally measuring 150 cm × 120 cm × 110 cm has . . .

Question : 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?

Doubt by Yathartha, Saumya

Solution : 
Dimensions of Cuboidal Cistern
L = 150 cm

B = 120 cm

H = 110 cm

Total volume of the cistern = LBH
= 150×120×110
= 1980000 cm³

Volume of water present in the cistern = 129600 cm³

Volume of water required to fill the cistern
= 1980000 - 129600
= 1850400 cm³

Dimensions of each brick 
l = 22.5 cm

b = 7.5 cm

h = 6.5 cm

Volume of each brick
= 22.5×7.5×6.5
= 1096.875  cm³

Let the number of bricks required to fill the cistern up to the brim = n

Volume of water increased by 1 bricks
= Volume of 1 brick - 1/17(Volume of 1 brick)
= Volume of 1 brick (1-1/17)
= Volume of 1 brick (16/17)

= 1096.875×(16/17) 

Volume of water increased by n bricks
= 1096.875×(16/17)×n — (1)

Volume of water required to fill the cistern 

= 1850400 cm³ — (2)

Equating eq (1) and (2)

1096.875×(16/17)×n = 1850400 
n = (1850400 × 17) / (16×1096.875) 
n = 31456800/17550
n = 1792.41 
n = 1792 (approx)

Hence, 1792 bricks can be put in to the cistern without overflowing the water.