A wall $24 \mathrm{~m}$ long, $0.4 \mathrm{~m}$ thick and $6 \mathrm{~m}$ high is constructed with the bricks each of dimensions $25 \mathrm{~cm} \times 16$ $\mathrm{cm} \times 10 \mathrm{~cm}$. If the mortar occupies $\frac{1}{6}$ th of the volume of the wall, then find the number of bricks used in constructing the wall.
Given that, a wall is constructed with the help of bricks and mortar.
$\therefore$ Number of bricks $=\frac{\text { (Nolume of wall) }-\left(\frac{1}{10} \text { th volume of wall }\right)}{\text { Volume of a brick }}$...(i)
Also, given that
Length of a wall $(l)=24 \mathrm{~m}$,
Thickness of a wall $(b)=0.4 \mathrm{~m}$,
Height of a wall $(h)=6 \mathrm{~m}$
So, volume of a wall constructed with the bricks $=l \times b \times h$
$=24 \times 0.4 \times 6=\frac{24 \times 4 \times 6}{10} \mathrm{~m}^{3}$
Now,$\frac{1}{10}$ th volume of a wall $=\frac{1}{10} \times \frac{24 \times 4 \times 6}{10}=\frac{24 \times 4 \times 6}{10^{2}} \mathrm{~m}^{3}$
and Length of a brick $\left(l_{l}\right)=25 \mathrm{~cm}=\frac{25}{100} \mathrm{~m}$
Breadth of a brick $\left(b_{1}\right)=16 \mathrm{~cm}=\frac{16}{100} \mathrm{~m}$
Height of a brick $\left(h_{1}\right)=10 \mathrm{~cm}=\frac{10}{100} \mathrm{~m}$
So, volume of a brick $=l_{1} \times b_{1} \times l_{1}$
$=\frac{25}{100} \times \frac{16}{100} \times \frac{10}{100}=\frac{25 \times 16}{10^{5}} \mathrm{~m}^{3}$
From Eq. (i),
Number of bricks $=\frac{\left(\frac{24 \times 4 \times 6}{10}-\frac{24 \times 4 \times 6}{100}\right)}{\left(\frac{25 \times 16}{10^{5}}\right)}$
$=\frac{24 \times 4 \times 6}{100} \times 9 \times \frac{10^{5}}{25 \times 16}$
$=\frac{24 \times 4 \times 6 \times 9 \times 1000}{25 \times 16}$
$=24 \times 6 \times 9 \times 10=12960$
Hence, the required number of bricks used in constructing the wall is 12960.