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Given details are,

Amount of tin in an alloy = 15 parts

Amount of copper in an alloy = 105 parts

So, total weight of alloy = 15 + 105 = 120 parts

Now, by calculating

Percentage of copper in alloy = (105/120) × 100

= 525/6

= 87.50%

∴ Percentage of copper in an alloy is 87.50%

Let x% of y is y% of Z 

∴ x/100 × y = y/100 × Z 

⇒ x y/100 = y/100 × Z 

⇒ Z = x y/100 × 100/y 

⇒ Z = x

Let the marked price = ‘x

∴ x + 15% of x = 3450

⇒ 115x/100 = 3050 ⇒ x = 3000

∴ Market price of the article = Rs. 3000

Since new sales tax = 60%

Now the customer will pay = Rs 3000 + 6% of RS 3000 = 106/100 × RS 3000 = Rs 3180 

∴ customer will pay for the article = 3450 – 3180 = 270 less

(i) 25%

To convert percentage to fractions we have to divide by 100,

i.e., 25/100 = 1/4 or 1:4

(ii) 2.5%

To convert percentage to fractions we have to divide by 100,

i.e., 2.5% can be written as 25/10

so, (25/10)/100 = 25/1000 = 1/40 or 1:40

(iii) 0.25%

To convert percentage to fractions we have to divide by 100,

i.e., 0.25% can be written as 25/100

so, (25/100)/100 = 25/10000 = 1/400 or 1:400

(iv) 0.3%

To convert percentage to fractions we have to divide by 100,

i.e., 0.3% can be written as 3/10

so, (3/10)/100 = 3/1000 or 3:1000

(v) 125%

To convert percentage to fractions we have to divide by 100,

i.e., 125/100 = 5/4 or 5:4

(i) 27%

To convert percentage to decimal fractions we have to divide by 100,

i.e., 27% = 27/100 = 0.27

(ii) 6.3%

Here 6.3 can be written as 63/10

To convert percentage to decimal fractions we have to divide by 100,

i.e., 6.3% = 63/(10 × 100) =63/1000 = 0.063

(iii) 32%

To convert percentage to decimal fractions we have to divide by 100,

i.e., 32% = 32/100 = 0.32

(iv) 0.25%

Here 0.25 can be written as 25/100

To convert percentage to decimal fractions we have to divide by 100,

i.e., 0.25% = 25/(100 × 100) = 25/10000 = 0.0025

(v) 7.5%

Here 7.5 can be written as 75/10

To convert percentage to decimal fractions we have to divide by 100,

i.e., 7.5% = 75/(10 × 100) =75/1000 = 0.075

(vi) 1/8%

To convert percentage to decimal fractions we have to divide by 100,

i.e., 1/8% = 1/(8 × 100) =1/800 = 0.00125

(i) 27% 

The required decimal fraction is,\(=\frac{27}{100}\)=0.27.

(ii) 6.3%

 The required decimal fraction is,\(=\frac{63}{10\times100}\)=0.063.

(iii) 32%

 The required decimal fraction is,\(=\frac{32}{100}=\frac{8}{25}\)0.32.

(iv) 7.5% 

The required decimal fraction is,\(=\frac{75}{10\times100}=\frac{3}{40}\)=0.075.

(v)\(\frac{1}{8}\)%

The required decimal fraction is,\(=\frac{1}{8\times100}\)=0.00125.

Let cost price of Chinese Vase before hike be = Rs x

The hike is = 20% of 100 = 20/100

The cost price of Chinese Vase after hike is = Rs 2000

So, let’s calculate for x,

x + x×20/100 = 2000

x + x/5 = 2000

(5x+x)/5 = 2000

6x = 2000×5

x = 10000/6

= 1666.6667

∴ Original price of Chinese Vase is = Rs. 1666.67

(i) Given (3/4)

= (3/4) × 100

= 75%

(ii) Given (53/100)

= (53/100) × 100

= 53%

(iii) Given 1 (3/5)

Convert the given mixed fraction into improper fraction

1 (3/5) = (8/5)

= (8/5) × 100

= 160%

(iv) Given (7/20)

= (7/20) × 100

= 35%

(i) Given 2.5%

= (2.5/100)

= (25/1000)

= (1/40)

(ii) Given 0.4%

= (0.4/100)

= (4/1000)

= (1/250)

(iii) Given 13 (3/4) %

13 (3/4) = 13.75

= 13.75/100

= 1375/10000

= 11/80

(i) Given 45%

= (45/100)

On simplifying the above fraction we get

= (9/20)

(ii) Given 0.25%

= (0.25/100)

= (25/10000)

On simplifying the above fraction we get

= (1/400)

(iii) Given 150%

= (150/100)

On simplifying the above fraction we get

= (3/2)

(iv) Given 6 (1/4) %

We can write 6 (1/4) as 6.25

= (6.25/100)

= (625/1000)

= (1/16)

Let the total number of students be 100

Then, as per the question 70% of boys = 70

Number of girls = 30

Now, total number of students when the number of girls is 30 = 100

Then, total number of students when the number of girls is 504 = (100/30) × 504

= 1680

Total number of boys = 1680 – 504

= 1176

∴the number of boys in a school is 1176

(i) Number of coloured square = 58 

Total number of squares = 100 

∴ Fraction : \(\frac{58}{100}\)

Decimal : 0.58 

Percentage : 58%

(ii) Number of coloured square = 53 

Total number of squares = 100 

∴ Fraction : \(\frac{53}{100}\)

Decimal : 0.53 

Percentage : 53% 

(iii) Number of coloured square = 25 

Total number of squares = 50 

∴ Fraction : \(\frac{25}{50}\)

Decimal : \(\frac{25}{50}\) x \(\frac{2}{2}\) 

= \(\frac{50}{100}\)

= 0.50

Percentage : \(\frac{25}{50}\) x \(\frac{100}{100}\) = \(\frac{25}{50}\) x 100% 

= 50%

(iv) Number of coloured square = 17 

Total number of squares = 25 

∴ Fraction : \(\frac{17}{25}\)

Decimal : \(\frac{17}{25}\) x \(\frac{4}{4}\) = \(\frac{68}{100}\)

= 0.68 

Percentage : \(\frac{17}{25}\) x \(\frac{100}{100}\) = \(\frac{17}{25}\) x 100% 

= 68%

(v) Number of coloured square = 15 

Total number of squares = 30 

∴ Fraction : \(\frac{15}{30}\)

Decimal : \(\frac{15}{30}\) = \(\frac{1}{2}\) x \(\frac{50}{50}\)

= \(\frac{50}{100}\)

= 0.50 

Percentage : \(\frac{15}{30}\) = \(\frac{15}{30}\) x \(\frac{100}{100}\) 

= \(\frac{15}{30}\) x 100%

= 50 %

Number of students who are good at science = 72% of 25 

= \(\frac{72}{100}\) x 25 

= 18 students 

∴ Number of students who are not good at science = 25 – 18 

= 7 students

(i) 88 % = \(\frac{88}{100}\)

= 0.88 

(ii) 1.86 % = \(\frac{1.86}{100}\)

= 0.0186

Total length of the cloth = 100 m 

Length of cloth bought = 72.3 m 

Percentage of cloth bought = \(\frac{72.3}{100}\)

= 72.3 %

Total plants = 1000 

Number of rose plants = 5 % of 1000 

= \(\frac{5}{100}\) x 1000 

= 50 

Number of Daisy plants = 1 % of 1000 

= \(\frac{1}{100}\) x 1000 

= 10 

Total of rose and daisy = 50 + 10 

= 60 

Number of other plants = 1000 – 60 

= 940

135 % of 80 = \(\frac{135}{100}\) x 80 

= Rs 108

Distance travelled by car = 80 km. 

Distance travelled by train = 320 km 

Total distance = 80 + 320 km 

= 400 km 

Percentage of distance travelled by car = \(\frac{800}{400}\) x 100 % 

= 20 % 

Percentage of distance travelled by train = \(\frac{320}{800}\) x 100 % 

= 40 %

Peters score = 280 marks 

Marks needed for a pass = 20 

∴ Total marks required to get a pass = 280 + 20 

= 300 

i.e. 50% of total marks = 300 

\(\frac{50}{100}\) x Total marks = 300  

\(\frac{1}{2}\) x Total Marks = 300

Total Marks = 300 x 2 

= 600 

Total marks of the exam = 600

(b) ₹ 16000

Because,

Let original salary of man be ₹ x

Increases salary him = 25%

The value increased = 25% of ₹ x

= (25/100) × x

= (25x/100)

= (x/4)

Salary after increment = (x + (x/4))

= (4x + x)/4

= (5x/4)

His increased salary = ₹ 20000

= (5x/4) = 20000

= x = (20000 × 4) / 5

= x = 4000 × 4

= x = ₹ 16000

(c) 40%

Because,

= (2/5) ×100

= (2/1) × 20

= 40%

(b) ₹ 20000

Because,

Let the gross value of TV be ₹ x

Commission on TV = 10%

Price of the TV after deducting the commission = ₹ (x – 10% of x)

= (x – ((10/100) × x))

= (x – (x/10))

= (10x – x)/10

= (9x/10)

The price of TV after deducting the commission = ₹ 18000

= (9x/10) = 18000

= x = (18000 ×10) / 9

= x = (2000 × 10)

= x = ₹ 20000

Monthly salary of Mr. Sharma = Rs 8000

He spends every month = ₹ 6400

His savings = Rs 8000 – 6400 = Rs 1600

(i) Percent expenditure = 6400/8000 x 100% = 80%

(ii) Percent savings = 1600/8000  x 100% = 20%

Percentage = (0.05/20 × 100) % 

= (0.05 × 5) % 

= 0.25%

2 liters = 2 x 1000 

= 2000 mL 

Now, 

Percentage = (250 /2000 x 100) % 

= (250 /20) % [Divided by 100] 

= 12.5 %

10 kg = 10 × 1000 = 10000 g 

Let Z% of 1000 is 250 

∴ Z/100 × 10000 = 250 

⇒ 100 Z = 250 

⇒ Z = 250/100 

⇒ Z = 2.5%

Percentage = {(1/45)/(2/9) × 100} % 

= {1/45 × 9/2 × 100} % 

= {1/5 × 1/2 × 100} % 

= {1/5 × 50} % 

= 10%

Percentage = (48/320 × 100) % 

= (48/32 × 10) % 

= (3/2 × 10) % 

= 15%

Percentage = (54/45 × 100) % 

= (54/9 × 20) % 

= (6 × 20) % 

= 120%

Let number = Z 

Then, 

5% of Z = 9 

⇒ 5/100 × Z = 9 

⇒ 5 Z = 900 

⇒ Z = 180

Percentage = (54/45 × 100) % 

= (54/9 × 20) % 

= (6 × 20) % 

= 120%

6 : 5 = 6/5 

= (6/5 × 100) % [100% = 1] 

= (6 × 20) % 

= 120 %

Let population of the town a year ago = Z 

∴ Present population = 108% of Z 

⇒ 54000 = Z × 108/100 

⇒ 54000 = Z × 27/25 

⇒ Z = 54000 × 25/27 

⇒ Z = 2000 × 25 

⇒ Z = 50000

Present population of town = 60000 

Percentage increase in population annually = 10%

 Hence , 

Population of town after 2 years = present population \(\times[{\frac{100+\text{% increase}}{100}}]\)^time (time in years)

\(={60000}\times\frac{100+10}{100}\times\frac{100+10}{100}\)

\(={60000}\times\frac{110}{100}\times\frac{110}{100}\)

= 72600

Present value of machine = Rs.100000 

Depreciation in price every year = 5% 

Hence,

\(={100000}\times\frac{100-5}{100}\times\frac{100-5}{100}\)

\(={100000}\times\frac{95}{100}\times\frac{95}{100}\)

= Rs.90250

Number of beads received = 50 

Number of brown beads = 5 

Percentage of brown beads = \(\frac{15}{50}\) x 100 % 

= 10 % 

10% of the beads was brown.

Given details are,

Present value of machine is = Rs 100000

Every year the depreciation in price is = 5%

So, value after two years = 100000 × (100-5)/100 × (100-5)/100

= 100000 × 95/100 × 95/100

= 90250

∴ Value of machine after two years is Rs 90250.

Number of Matches won = 70 

Number of Matches lost = 28 

“No result” Matches = 2 

Total Matches = 70 + 28 + 2 

= 100

Percentage of Matches won = \(\frac{70}{100}\) x 100 %

= 70 % 

The won 70% of the matches

Total number of magazines in the bookstore = 100 m 

Number of comedy magazines = 14 

Percentage of comedy magzines = \(\frac{14}{70}\) x 100% 

= 20% 

20% of the magazines are comedy magazines.

Let the marked price of the raincoat be Rs P 

Amount he paid at a discount of 25% = Rs 1000 

(Marked Price) – (25% of P) = 1000 

P – (\(\frac{25}{100}\) x P) = 1000 

P – \(\frac{1}{4}\) x P = 1000

P (1 – \(\frac{1}{4}\)) = 1000 

\(\frac{3}{4}\)P = 1000 

P = 1000 x \(\frac{4}{3}\)

= \(\frac{4000}{3}\)

P = 1333.33 

∴ Marked price of the shoes = Rs 1333

Height of flag pole = 6.75 m 

= \(\frac{675}{100}\)

= 6.75%

Population of the village = 8000 people 

Literate people = 80 % of population 

= 80 % of 8000 

= \(\frac{80}{100}\) x 8000 

Literate people = 6400 

Percentage of women = 40 % 

Number of women = 40 % of literate people 

= \(\frac{40}{100}\) x 6400 

= 2560 

∴ Literate women : Total population

= 8000 : 2560 

= 25 : 8

Capacity of the tank = 50 litres 

Amount of water filled = 30% of 50 litres 

= \(\frac{30}{100}\) x 50 

= 15 litres 

Amount of water to be filled = 50 – 15 

= 35 litres

(i) 0.282 = 0.282 x 100% 

= \(\frac{282}{100}\) x 100 % 

= 28.2 %

(ii) 1.51 = \(\frac{151}{100}\) x 100 % 

= 151 %

(iii) 1.09 = \(\frac{109}{100}\) x 100 % 

= 109 %

(iv) 0.71 = \(\frac{71}{100}\) x 100 % 

= 71 %

(v) 0.858 = \(\frac{858}{1000}\) x 100 % 

= 85.8 %

Suppose Gayathri had Rs X in the beginning. 

Then money Spend = 75 % of X 

= \(\frac{75}{100}\)X 

= \(\frac{3X}{4}\)

Money left with her 

= X – \(\frac{3X}{4}\)

= \(\frac{4X-3X}{4}\)

= \(\frac{X}{4}\)

But it is given that money left = Rs 600 

i.e. \(\frac{X}{4}\) = 600 

X = 600 x 4 

= 2400 

∴ Gayathri had Rs 2,400

16\(\frac{2}{3}\) = \(\frac{50}{30}\)

= \(\frac{50}{30}\) x 100 % 

= 1666.67 %

⇒ \(\frac{2}{5}\) 

= \(\frac{2}{5}\) x 100 

= 40 % 

0.17 = \(\frac{17}{100}\)

= 17 % 

∴ 1666.67 is greater 

∴ 16\(\frac{2}{3}\) is greater

Capacity of the water tank = 200 litres 

Percentage of water in the tank = 40% 

Percentage of water to fill = Upto 75%

Difference in percentage = 75 % – 40 % 

= 35 % 

∴ Volume of water to be filled = Percentage of difference x total capacity 

= \(\frac{35}{100}\) x 200 

= 70 l 

70 l of water to be filled

Given, number of days Deepti went to school = 216 days

Deepti Attendance percentage is = 90%

So, let the number of days when school remained opened be x days

Hence,

(x × 90)/100 = 216

By using cross multiplication we get,

x = (216×100)/90

= 240 days

∴ Number of days the school remained opened for 240 days.

Number of days she went to school = 216 days 

Attendence percentage = 90%

 Let number of days for which school was opened = x 

Hence,

\(=\frac{x\times90}{100}=216 \)

\(={x}=\frac{216\times100}{90} =240\) days

Let B’s income = 100 

Then, A’s income = (100 – 20) = 80 

∴ B’s income more than A’s income = (100 – 80)/80 × 100 

= 20/80 × 100 

= 1/4 × 100 

= 25