Find the number of bricks, each measuring 25 cm × 12.5 cm × 7.5 cm, required to construct a wall 6 m long, 5 m high and 50 cm thick, while the cement and the sand mixture occupies $\dfrac{1}{20}\text{ th}$ of the volume of the wall.

Given,

Dimensions of wall :

Length = 6 m = 600 cm.

Height = 5 m = 500 cm

Thickness = 50 cm.

Dimension of brick :

Length = 25 cm

Breadth = 12.5 cm

Height = 7.5 cm

Calculating the volume of the wall,

Total volume of the wall = l × b × h

= 600 × 500 × 50

= 1,50,00,000 cm³.

Calculating the volume of bricks,

Volume of bricks = Volume of the wall - $\dfrac{1}{20}$ th volume of the wall (occupied by sand and cement)

= 1,50,00,000 - $\dfrac{1}{20}$ × 1,50,00,000

= 1,50,00,000 - 7,50,000

= 1,42,50,000 cm³.

Calculating volume of one brick,

Volume of one brick = l × b × h

= 25 × 12.5 × 7.5

= 2343.75 cm³.

Number of bricks = $\dfrac{\text{Total volume of the bricks}}{\text{Volume of one brick}}$

= $\dfrac{1,42,50,000}{2343.75}$

= 6080.

Hence, number of bricks = 6080.