Question

What will be the cost of bricks at Rs.350 per 1000 bricks if each of dimension
25cm16cm10cm is needed to build a 24m6m0.4m wall when 10% of the wall is filled with
mortar?
A) 4000Rs
B) 4500Rs
C) 4536Rs
D) 4636Rs

Answer 1

Hint: Find the volume of the wall and deduct \[10\% \] of the wall which is filled with mortar, and find the volume of a single brick and divide both to find the number of bricks used in the wall and find the cost using the condition given.

Complete step-by-step answer:
Given, Cost of 1000 bricks is Rs.350.
So, the cost of a single brick is \[Rs0.35\] .
Dimensions of a single brick is \[25cm \times 16cm \times 10cm\] ,
Here L = 25cm, B = 16cm, and W = 10cm.
Let’s use it and calculate the volume of the single brick.
So, the volume of a single brick is \[25cm*16cm*10cm = 4000c{m^3}\] .
Dimensions of the wall is \[24m \times 6m \times 0.4m\] ,
Here L = 25cm, B = 16cm, and W = 10cm.
Let’s use it and calculate the volume of the single brick.
So, the volume of the wall is \[24m*6m*0.4m = 57.6{m^3}\] .
Provided \[10\% \] of the wall is filled with mortar, so the volume of the mortar used in the wall is
\[ \Rightarrow 10\% {\rm{ }}of{\rm{ }}57.6\]
\[ \Rightarrow \dfrac{{10}}{{100}}*57.6\]
\[ \Rightarrow 5.76{m^3}\]
So, the volume of the mortar used in the wall is \[5.76{m^3}\] .
So, the volume of the bricks used in the wall is \[57.6{m^3} - 5.76{m^3} = 51.84{m^3}\]
Number of bricks used in the wall= (Volume of the wall excluding \[10\% \] volume of mortar) / (Volume of a single brick).
Number of bricks used in the wall is,
\[ \Rightarrow \dfrac{{51.84{m^3}}}{{4000c{m^3}}}\]
\[ \Rightarrow \dfrac{{51.84 \times 1000000}}{{4000}}\]
\[ \Rightarrow 12960Bricks\]
So, 12960 bricks were used in the wall.
If 1000 bricks costs Rs.350, then 1 brick costs Rs. \[\dfrac{{350}}{{1000}}\] .
So, the cost of a single brick is \[Rs0.35\] .
So, the cost of 12960 bricks is=\[0.35 \times 12960 = Rs4536\] .
That means Option C is correct \[Rs4536\] .

Note: When \[n\] units cost \[Rs.x\] , then 1 unit costs \[Rs\dfrac{x}{n}\] . Wall contains bricks and mortar, to calculate the volume of bricks used, the volume of mortar has to be deducted for the exact volume of bricks used in the wall.