Question

A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions $25cm\times 16cm\times 10cm$. If the mortar occupies $\frac{1}{10}th$ of the volume of the wall, then find the number of bricks used in constructing the wall.

• A. 11960
• B. 12960
• C. 15620
• D. 8890

Answer 1

The correct option is B

12960

Given that , a wall is constructed with the help of bricks and mortar.
Also, given that
Length of a wall (l) = 24 m
Thickness of a wall (b) = 0.4 m
Height of a wall (h) = 6 m
So, volume of a wall constructed with the bricks $=l\times b\times h$
$=24\times 0.4\times 6=\frac{24\times 4\times 6}{10}{m}^{3}Now,\frac{1}{10}thVolumeofawall=\frac{1}{10}\times \frac{24\times 4\times 6}{10}{m}^{3}andLengthofabrick\left(1_1\right)=25cm=\frac{25}{100}mBreadthofbrick\left(b_1\right)=16cm=\frac{16}{100}mHeightofabrick\left(h_1\right)=10cm=\frac{10}{100}mSo,Volumeofabrick=1_1\times b_1\times h_1=\frac{25}{100}\times \frac{16}{100}\times \frac{25\times 16}{{10}^6}{m}^3$
$Numberofbricks=\frac{\left(Volumeofwall\right)-\left(\frac{1}{10}thvolumeofwall\right)}{Volumeofabrick}$
$Numberofbricks=\frac{(\frac{24\times 4\times 6}{10}-\frac{24\times 4\times 6}{100})}{\left(\frac{25\times 16}{{10}^5}\right)}\frac{24\times 4\times 6}{100}\times 9\times \frac{{10}^5}{25\times 16}=\frac{24\times 4\times 6\times 9\times 1000}{25\times 16}=24\times 6\times 9\times 10=12960$
Hence, the required number of bricks used in constructing the wall is 12960.