Q.1

Express the following as a fraction : 0.008%

Explanation :
0.008 = 8/100 = 1/1250.

Q.2

Express the following as a Decimal : 0.04%

Explanation :
0.04%= 0.04/100 =0.004.

Q.3

Express the following as rate percent :0.004

Explanation :
0.004 = [(4/1000)*100]% = 0.4%.

Explanation :
28% of 450 + 45% of 280 =[(28/100)*450 + (45/100)*280] = (126+126) =252.

Q.5

What percent of 2 metric tones is 40 quintals ?

Explanation :
1 metric tonne = 10 quintals. Required percentage = [ (40/(2 * 10)) * 100]% = 200%.

Q.6

Find the missing figures :?% of 25 = 20125

Explanation :
Let x% of 25 = 2.125. Then , (x/100)*25 = 2.125 X = (2.125 * 4) = 8.5.

Q.7

If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?

Explanation :
Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14.

Q.8

An inspector rejects 0.08% of the meters as defective. How many will be examine to project ?

Explanation :
Let the number of meters to be examined be x.
Then, 0.08% of x =2
[(8/100)*(1/100)*x] = 2
x = [(2*100*100)/8] = 2500

Q.9

Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?

Explanation :
Let the number be x. Then, 4*x/5 –(65% of x) = 21 4x/5 –65x/100 = 21
5 x = 2100
x = 140.

Q.10

Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number , find the number ?

Explanation :
. Let the numbers be x and y. Then , 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150.

Q.11

In expressing a length 810472 km as nearly as possible with three significant digits , find the percentage error.

Explanation :
Error = (81.5 – 81.472)km = 0.028.
Required percentage = [(0.028/81.472)*100]% = 0.034%.

Q.12

In an election between two candidates, 75% of the voters cast thier thier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.

Explanation :
Let the number of votes enrolled be x. Then ,
Number of votes cast =75% of x. Valid votes = 98% of (75% of x). 75% of (98% of (75%of x)) =9261.
[(75/100)*(98/100)*(75/100)*x] =9261.
X = [(9261*100*100*100)/(75*98*75)] =16800.

Q.13

Shobha’s mathematics test had 75 problems i.e.10 arithmetic, 30 algebra and 35 geometry problems. Although she answered 70% of the arithmetic ,40% of the algebra, and 60% of the geometry problems correctly. she did not pass the test because she got less than 60% of the problems right. How many more questions she would have to answer correctly to earn 60% of the passing grade?

Explanation :
Number of questions attempted correctly=(70% of 10 + 40% of 30 + 60% 0f 35) =7 + 12+21= 45
questions to be answered correctly for 60% grade=60% of 75 = 45
therefore required number of questions= (45-40) = 5.

Q.14

If 50% of (x-y) = 30% of (x+y) then what percent of x is y?

Explanation :
50% of (x-y)=30% of(x+y)
(50/100)(x-y)=(30/100)(x+y)
5(x-y)=3(x+y)
2x=8y
x=4y
therefore required percentage =((y/x) X 100)% = ((y/4y) X 100) =25%

Q.15

Mr.Jones gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to his 3 sons. half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. how much money did Mr.jones have initially?

Explanation :
Let the initial amount with Mr.jones be Rs.x then,
Money given to wife= Rs.(40/100)x=Rs.2x/5
.Balance=Rs(x-(2x/5)=Rs.3x/5.
Money given to 3 sons= Rs(3X((20/200) X (3x/5)) = Rs.9x/5.
Balance = Rs.((3x/5) – (9x/25))=Rs.6x/25.
Amount deposited in bank= Rs(1/2 X 6x/25)=Rs.3x/25. Therefore 3x/25=12000
x= ((12000 x 35)/3)=100000 So Mr.Jones initially had Rs.1,00,000 with him.

Q.16

10% of the inhabitants of village having died of cholera.,a panic set in , during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.

Explanation :
Let the total number of orginal inhabitants be x.
((75/100))*(90/100)*x)=4050
(27/40)*x=4050 x=((4050*40)/27)=6000.

Q.17

A salesman`s commission is 5% on all sales upto Rs.10,000 and 4% on all sales exceeding this.He remits Rs.31,100 to his parent company after deducing his commission . Find the total sales.

Explanation :
Let his total sales be Rs.x.Now(Total sales) – (Commission )=Rs.31,100 x-[(5% of 10000 + 4% of (x-10000)]=31,100
x-[((5/100)*10000 + (4/100)*(x-10000)]=31,100
x-500-((x-10000)/25)=31,100
x-(x/25)=31200
24x/25=31200x=[(31200*25)/24)=32,500.
Total sales=Rs.32,500

Q.18

Raman`s salary was decreased by 50% and subsequently increased by 50%.How much percent does he lose?

Explanation :
Let the original salary = Rs.100
New final salary=150% of (50% of Rs.100)= Rs.((150/100)*(50/100)*100)=Rs.75.
Decrease = 25%

Q.19

Paulson spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings .

Explanation :
Let the original income=Rs.100
. Then , expenditure=Rs.75 and savings =Rs.25 New income =Rs.120 ,
New expenditure = Rs.((110/100)*75)=Rs.165/2
New savings = Rs.(120-(165/2)) = Rs.75/2
Increase in savings = Rs.((75/2)-25)=Rs.25/2
Increase %= ((25/2)*(1/25)*100)% = 50%.

Q.20

The salary of a person was reduced by 10% .By what percent should his reduced salary be raised so as to bring it at par with his original salary ?

Explanation :
Let the original salary be Rs.100 . New salary = Rs.90. Increase on 90=10 , Increase on 100=((10/90)*100)% = (100/9)%

Q.21

When the price fo a product was decreased by 10% , the number sold increased by 30%. What was the effect on the total revenue ?

Explanation :
Let the price of the product be Rs.100 and let original sale be 100 pieces.
Then , Total Revenue = Rs.(100*100)=Rs.10000.
New revenue = Rs.(90*130)=Rs.11700.
Increase in revenue = ((1700/10000)*100)%=17%.

Q.22

. If the numerator of a fraction be increased by 15% and its denominator be diminished by 8% , the value of the fraction is 15/16. Find the original fraction.

Explanation :
Let the original fraction be x/y.
Then (115%of x)/(92% of y)=15/16 => (115x/92y)=15/16
((15/16)*(92/115))=3/4

Q.23

In the new budget , the price of kerosene oil rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase ?

Explanation :
Reduction in consumption = [((R/(100+R))*100]%
[(25/125)*100]%=20%.

Q.24

The population of a town is 1,76,400 . If it increases at the rate of 5% per annum , what will be its population 2 years hence ? What was it 2 years ago ?

Explanation :
Population after 2 years = 176400*[1+(5/100)]^2 =[176400*(21/20)*(21/40)]
= 194481.
Population 2 years ago = 176400/[1+(5/100)]^2
=[716400*(20/21)*(20/21)]= 160000.

Q.25

During one year, the population of town increased by 5% . If the total population is 9975 at the end of the second year , then what was the population size in the beginning of the first year ?

Explanation :
Population in the beginning of the first year = 9975/[1+(5/100)]*[1-(5/100)] = [9975*(20/21)*(20/19)]=10000.

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