Let the positive number be x.Accordingtothequestion,x×x=x+(x×2000)100x2=x+20xx2−21x=0Either,x=0,orx=2121isthepossiblevalue.Thensquareof21is441.$$\begin{array}{rl}& \text{Let the positive number be x}.\\ & \text{According}\phantom{\rule{thinmathspace}{0ex}}\text{to}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{question},\\ & x\times x=x+\frac{\left(x\times 2000\right)}{100}\\ & {x}^{2}=x+20x\\ & {x}^{2}-21x=0\\ & \text{Either},\\ & x=0,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}or\\ & x=21\\ & \text{21}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{possible}\phantom{\rule{thinmathspace}{0ex}}\text{value}\text{.}\\ & \text{Then}\phantom{\rule{thinmathspace}{0ex}}\text{square}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}21\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}441.\end{array}$$
Let the number of people be x who has been asked for the donations.
People already solicited = 60% of x = 0.6x
Remaining people = 40% of x = 0.4x
Amount collected from the people solicited, = 600 *0.6x = 360x
360x = 75% of the amount collected.
Remaining amount = 25% = 120x
Thus,
Average donations from remaining people,
= 120x /0.4x = 300.
Actualresult=10xBymistakeithasbeendividedby10=x10%change=[10x−(10x)10x]×100=99=−99%Since, actual value is greater than the wrong value.Alternatively,Let,x=10Actualresult=10×10=100Wrongresult=1010=1Change=(1−100)=−99%change=−99%$$\begin{array}{rl}& \text{Actual}\phantom{\rule{thinmathspace}{0ex}}\text{result}=10x\\ & \text{By}\phantom{\rule{thinmathspace}{0ex}}\text{mistake}\phantom{\rule{thinmathspace}{0ex}}\text{it}\phantom{\rule{thinmathspace}{0ex}}\text{has}\phantom{\rule{thinmathspace}{0ex}}\text{been}\phantom{\rule{thinmathspace}{0ex}}\text{divided}\phantom{\rule{thinmathspace}{0ex}}\text{by}\\ & 10=\frac{x}{10}\\ & \mathrm{\%}\phantom{\rule{thinmathspace}{0ex}}\text{change}=\left[\frac{10x-\left(\frac{10}{x}\right)}{10x}\right]\times 100=99\\ & =-99\mathrm{\%}\\ & \text{Since, actual value is greater than the wrong value}\text{.}\\ & \\ & \text{Alternatively,}\\ & \text{Let},\phantom{\rule{thinmathspace}{0ex}}x=10\\ & \text{Actual}\phantom{\rule{thinmathspace}{0ex}}\text{result}=10\times 10=100\\ & \text{Wrong}\phantom{\rule{thinmathspace}{0ex}}\text{result}=\frac{10}{10}=1\\ & \text{Change}=\left(1-100\right)=-99\\ & \mathrm{\%}\phantom{\rule{thinmathspace}{0ex}}\text{change}=-99\mathrm{\%}\end{array}$$
Copper : Aluminum = 7 : 4.
Let Copper and Aluminum in the weapon be 7x and 4x respectively.
Given,
Aluminum in weapon = 12 kg
So,
→ 4x = 12.
→ x = 3
Copper = 7x = 7 * 3 = 21 Kg.
Total alloy in the weapon = 12 + 21 = 33 kg
But 12% alloy get destroyed in making the weapon, i.e. 88% alloy is used in the weapon, so,
→ 88 % alloy = 33 kg
→ 100 % alloy = 37.5 kg.
Now, 55% of 600 passed in Chemistry = (55 X 600) / 100 = 330
From question, 40% of those who passed in Chemistry(330 Students) also passed in physics => (40 X 330) / 100 = 132 ,
so, 132 students passed in both
Therefore % who passed in both = (132 X 100 ) / 600 = 22%
Passed in both subject = 22% of total students
% of students who passed in either Physics or Chemistry or both, = (65 +55) -22 = 98%
Thus, percentage of students who failed in both subjects, = 2%
Number of students who failed = 2% of 600 = 12.