A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs
5 per bag of grey cement sold. (a) The company sells 3,000 bags of white cement and
5,000 bags of grey cement in a month. What is its profit or loss? (b) What is the number
of white cement bags it must sell to have neither profit nor loss, if the number of grey
bags sold is 6,400 bags.
Answers
Answer:
DEF are respectively the midpoints of sides AB, BC and CA of triangle ABC, then: Ratio of area of triangle DEF : area of triangle ABC = 1 : 4
Solution:
In the given question, we know Triangle DEF formed with midpoints is similar to the Outer Triangle ABC
On the basis of the similarity, we can say,
If two triangles are similar then the ratio of their area is equal to the square of the ratio of their corresponding sides
Mathematically can be written as :-
\frac{\text {area of triangle } D E F}{\text {area of triangle ABC}}=\left(\frac{D E}{A C}\right)^{2}
area of triangle ABC
area of triangle DEF
=(
AC
DE
)
2
Since, DECF is a parallelogram. So DE = FC
On substituting:
\frac{\text {area of triangle } D E F}{\text {area of triangle ABC}}=\left(\frac{F C}{A C}\right)^{2}
area of triangle ABC
area of triangle DEF
=(
AC
FC
)
2
Also, F is the midpoint of AC
\text { So } \mathrm{AC}=2 \times \mathrm{FC} So AC=2×FC
\begin{gathered}\begin{array}{l}{\frac{\text {area of triangle } D E F}{\text {area of triangle } A B C}=\left(\frac{F C}{2 F C}\right)^{2}} \\\\ {\frac{\text {area of triangle } D E F}{\text {area of triangle } A B C}=\frac{1}{4}}\end{array}\end{gathered}
area of triangle ABC
area of triangle DEF
=(
2FC
FC
)
2
area of triangle ABC
area of triangle DEF
=
4
1
Hence ratio of area of triangle DEF and triangle ABC is given as:
Ratio of area of triangle DEF : area of triangle ABC = 1 : 4
Learn more about midpoints of triangle
Find the vertices of a triangle, the midpoints of whose side are(3,1),(5,6,),(-3,2)
https://brainly.in/question/3073037
The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to what?
https://brainly.in/question/5968686
Given:-
A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.
To Find:-
(a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.
Solution:-
Profit gained by 1 bag of white cement = Rs 8
Loss of 1 bag of grey cement = Rs 5
(i) Profit from selling 3000 white cement bags = Rs 3000\times8\ =\ 240003000×8 = 24000
(ii) Loss from selling 5000 grey cement bags = Rs 5000\times5=\ 250005000×5= 25000
since 24000<2500024000<25000
profit\ <\ loss\profit < loss
Therefore, his total loss on selling the grey cement bags = loss\ -\ profit\loss − profit
25000-24000\ =\ 100025000−24000 = 1000
Thus, company has lost of Rs 1000 on selling the grey cement bags.
(b)
Let the no. of white cement bags be 'x'
According to the question
Loss = Profit
Therefore, 5\times6400\ =\ x\ \times85×6400 = x ×8
\frac{5\times6400}{8}=\ x85×6400= x
x=\ 4000x= 4000
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