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How many bricks of dimension $ 20cm \times 10cm \times 10cm $ are required to build a wall $ 12m $ long, $ 3m $ high and $ 30cm $ wide, if $ 10\% $ of the wall is made of mortar?
A. $ 4860 $
B. $ 5200 $
C. $ 4600 $
D. $ 5000 $

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Last updated date: 24th Jul 2024
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Answer
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Hint: Here first of all we will find the volume of the wall and the volume of one brick and also consider the percentage of the mortar in the wall. Make sure both have the same system of units and then take the ratio of both the volumes to get the count of the number of bricks.

Complete step-by-step answer:
Given the measures of the wall: $ 12m $ long, $ 3m $ high and $ 30cm $ wide,
Now, the volume of the wall $ = 12 \times 3 \times \dfrac{{30}}{{100}} $ (third measure being in cm placed its equivalent value in meters)
Simplify the above expression –
Volume of the wall $ = \dfrac{{1080}}{{100}} $
Shift the two decimal points from the right hand side to the left hand side of the equation –
Volume of the wall $ = 10.8{m^3} $
Given that $ 10\% $ of the wall is comprised of mortar
New volume of the wall comprised with bricks $ = 10.8 \times 90\% {\text{ }}{m^3} $
Simplify the above expression –
New volume of the wall comprised with bricks $ = 10.8 \times \dfrac{{90}}{{100}}{\text{ }}{m^3} $
Simplify the above expression –
New volume of the wall consisted of bricks $ = 9.72{\text{ }}{m^3} $ ….. (A)
Given that measures of one brick $ 20cm \times 10cm \times 10cm $
Volume of brick $ = 20 \times 10 \times 10 $
Find the product of the terms –
Volume of brick $ = 2000c{m^3} $
Convert the centimeter cube and meter cube –
Volume of brick $ = \dfrac{{2000}}{{1000000}}{m^3} $
Volume of brick $ = 0.002{m^3} $ ….. (B)
Number of bricks $ = \dfrac{{9.72}}{{0.002}} $
Simplify the above expression –
Number of bricks $ = 4860 $
From the given multiple choices – the option A is the correct answer.
So, the correct answer is “Option A”.

Note: When you take ration between two volumes always remember that they should be in the same system of units. Know the basic conversational ratios between the different quantities that are centimeter cube and meter cube and litres and so on.