8th Class Mathematics Percentage Percentage

Percentage

Category : 8th Class

*       Introduction

 

The word percent means per hundred. It can be defined as the fraction whose denominator is 100, then the numerator of the fraction is called percent. It is denoted by the symbol '%'. If we have to find the percentage of any number we usually find the quantity per hundred of the number. It may be of two type growth or depreciation. If the value increases then it is called growth on the other hand if it decreases then it is called depreciation.  

Percent can also be expressed as the ratio with its second term being 100 and the first term is equal to the given percent. In order to convert the given ratio into a percent, we have to convert the given ratio first into the fraction and then multiply the fraction by 100. Conversely if we have to convert the given percent into ratio, we first convert the percent into the fraction and then reduce it to the lowest term.  

 

 

 

\[x:y=\left( \frac{x}{y}\times 100 \right)%\]

Or \[x%=\frac{x}{100}=x:100\]

Percent can also be expressed in the form of decimal. In order to convert the given fraction into the decimal we divide the numerator with 100 and get the required decimal form or by simply putting the decimals two digit to the left of the numerator.

Thus, r% of the quantity y is \[=y\times \frac{r}{100}\]

  • If the price of the commodity increases by r%, then consumption must be reduced by \[\left( \frac{r}{100+r}\times 100 \right)%\] so that expenditure does not increase.
  • If the price of the commodity decreases by r%, then consumption must be increased by \[\left( \frac{r}{100-r}\times 100 \right)%\] So that expenditure does not decrease.
  • If the income of one person is r% more than other then other's income is lesser than first by \[\left( \frac{r}{100+r}\times 100 \right)%\]
  • If the income of one person is r% less than other then other's income is more than first by \[\left( \frac{r}{100-r}\times 100 \right)%\]
  • If the value of the item increases at the rate r%, then after n interval its value is \[{{\left( 1+\frac{r}{100} \right)}^{n}}\] P  and also the value of the   item before n interval was \[\frac{P}{{{\left( 1+\frac{r}{100} \right)}^{n}}}\].
  • If the value of the item decreases at the rate of r%, then after n intervals its value is \[{{\left( 1-\frac{r}{100} \right)}^{n}}\] and also the value of the item before n interval was \[\frac{1}{{{\left( 1-\frac{r}{100} \right)}^{n}}}\]  

 

 

 

  • In a world survey 44% of the kids around the world watch television before they go to bed.
  • Percent is a Latin word which means per centum which is equivalent to per 100.
  • Percentage is the result obtained by multiplying a quantity by percent.
  • Nearly 40% of the US currency in circulation was counterfeit by the end of the civil war.
  • Close to 73% of girls in Bangladesh are married by the age of 18 years.  

 

 

 

  • Percent means per hundred.
  • If the denominator of the fraction is 100 then percentage is equal to the numerator of the fraction.
  • A ration with its second term 100 is also called percent.
  • If we have to convert the given fraction into the percent then we multiply the fraction by 100.
  • To convert decimal into the percent we shift the decimal to the two digit right of the given decimal.
  • To convert the percent into the decimal we divide the given percent by 100.  

 

 

 

 

  Smith has a diary farm in which the number of cows increases at the rate of 5% per annum which results in the increase in the production level of the milk by 10% per annum. But the demand of the milk is increasing at the rate of increase of the population of the town. If initially the farm has 16,0000 cows then the number of cows needed after 4 years to fulfill the requirement of the milk is:

(a) 204481                                          

(b) 214481

(c) 194440                                           

(d) 194481

(e) None of these

 

Answer: (d)

Explanation:

The number of cows after four years = 160000 \[{{\left( 1+\frac{5}{100} \right)}^{4}}=194481\].  

 

 

  D. Bravo plans to grow trees in the piece of land in the backyard of his house. If he increases the number of trees by 10% per year in the backyard. After 2 years he finds that the number of trees in the backyard is 14641. Find the number of trees in the backyard when he started the plantation.

(a) 12,100                                           

(b) 15,550

(c) 16,500                                            

(d) 18,500

(e) None of these

 

Answer: (a)

Explanation:

The number of trees two years back is given by

\[=\frac{p}{{{\left( 1+\frac{r}{100} \right)}^{n}}}=\frac{14641}{{{\left( 1+\frac{10}{100} \right)}^{2}}}=12,100\]  

 

 

  The two numbers M and N are such that 60% of M is equal to the 20% of N, then N = ?% of M.

(a) 300                                                 

(b) 300          

(c) 400                                                  

(d) 100

(e) None of these

 

Answer: (a)

Explanation:

According to the question,

60% M = 20% N

\[\frac{60}{100}M=\frac{20}{100}N\]

\[3M=N\]

\[\therefore \]\[N=\frac{3\times 100}{100}M=300%\]  

 

 

The population of the city is 6000 and \[\frac{3}{12}\] of the population is male and rest of them are female. If the 38% of the male are married, then the percentage of married female in the city is:

(a) 10%                                                

(b) 15%         

(c) 25%                                                

(d) 35%                

(e) None of these

 

Answer: (a)

Explanation:

Number of male in the city is \[\frac{3}{12}\times \text{6}000=\text{15}00\].

Number of female in the city = 6000 -1500 = 4500.

Number of married male \[\text{=}\frac{30}{100}\times \text{15}00=\text{45}0\]

% of married female\[\text{=}\frac{450}{4500}\times \text{1}00=10%\]  

 

 

  Three friends Joe, Anderson and Anthony work in the same company and obtain the certain salaries. If their combined salary is Rs. 15680 and they spend 85%, 75% and 70% of their respective salaries and their saving are  6 : 8 : 10 respectively, then their salaries are:                 

(a) (Rs. 6258, Rs. 5249, Rs. 4173)                                

(b) (Rs. 5954.43, Rs. 4763.54, Rs. 4962.03)                       

(c) (Rs. 6079, Rs. 5462, Rs. 4139)                                

(d) (Rs. 5884.4, Rs. 5564.2, Rs. 4231.4)                                          

(e) None of these                                                

 

Answer: (b)                         

 

          

  An export company increases the salary of its employee by 30% a end of the financial year. But due to certain loss it has to revert back its order of increase in the salary of its employee and restore it to its or) situation. By what percent must the new salary be reduced to restore its original situation?

(a) 40%                                

(b) 25%

(c) 23.07%                          

(d) 35.25%                          

(e) None of these

 

Answer: (c)  

 

 

  The four number are such that x is 5% of y, y is 4% of z, and z is 3% of the value of \[x=500\], then find the value of w.

(a) \[\text{1}0,\text{333},\text{333}.\overline{\text{3}}\]                           

(b) \[\text{8},\text{333},\text{333}.\overline{\text{3}}\]

(c) \[\text{7},\text{333,333}.\overline{\text{3}}\]                                            

(d) \[\text{5},\text{333},\text{333}.\overline{\text{3}}\]

(e) None of these

 

Answer: (b)  

 

 

  If the medicine for acidity and stomach upset consists of 80% of alcohol, 6.2% of menthe oil, 4.4% of spearmint oil, 5.2% of chloroform and rest is other find the quantity of spearmint oil in 40 ml of the pack of the medicine in the bottle.

(a) \[3.025\,ml\]                                              

(b) \[1.02\,ml\]

(c) \[2.08\,ml\]                                 

(d) \[5.628\,ml\]

(e) None of these        

 

Answer: (c)  

 

 

  One of the major problems Maria faces in her house hold work is to maintain the monthly budget as the price of the articles is increasing day by. The increasing price of the articles increases her budget almost every month. Now she is not in position to increase her monthly budget any more even though the price is increasing and so she has to reduce her consumption. If in the current month the price of milk increases by 10% rice by 20% and fruits by 20%, then how much percent must Maria reduce her consumption of respective items so that her monthly expenditure remains the same?

(a) 12.6% 14.2%, 14.2%                 

(b) 9.98%, 8.26%, 8.26%

(c) 10.1%, 8.2%, 10%                      

(d) 9.09%, 16.6% 16.6%

(e) None of these

 

Answer: (d)  

 

 

  In a city 30% of people like basketball, 10% like hockey and rest like other games. If the total population of the city is 10 lakhs, then the number of people who likes other games is:

(a) 500000                                          

(b) 200000

(c) 300000                                           

(d) 75000

(e) None of these

 

Answer: (a)    

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