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

**Explanation :**0.04%= 0.04/100 =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.

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

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

**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.

**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

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

5 x = 2100

x = 140.

**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.

**Explanation :**Error = (81.5 – 81.472)km = 0.028.

Required percentage = [(0.028/81.472)*100]% = 0.034%.

**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.

**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.

**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%

**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.

**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.

**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=31200x=[(31200*25)/24)=32,500.

Total sales=Rs.32,500

**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%

**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%.

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

**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%.

**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

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

[(25/125)*100]%=20%.

**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.

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