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Let the number of days the school was opened = Z 

∴ Percentage of attendance = 85% of Z 

Now, 

85% of Z = 204 

⇒ 85/100 × Z = 204 

⇒ Z = 204 × 100/85 

⇒ Z = 204 × 20/17 [Divided by 5] 

⇒ Z = 12 × 20 

⇒ Z = 240

Total money received = Rs.(1350 + 650)

= Rs.2000

Amount received from Rohit = Rs.650

Reqd. percentage = (650/2000) x 100 = 32.5%

Let shalu’s income = Rs. X

 Hence, shikha’s income 

\(={X}+{X}\times\frac{60}{100}\)

\(={X}+\frac{3X}{5}\)

\(=\frac{8X}{5}\)

Difference between shikha’s and shalu’s income

\(=\frac{8X}{5}-{X}\)

\(=\frac{3X}{5}\)

Hence, 

Percentage in which shalu’s income is less than shikha’s income

\(=\frac{\frac{3X}{5}}{\frac{8X}{5}}\times{100}\)

\(=\frac{75}{2}\)

= 37.5%

(i) According to the question required percentage = (6/24) × 100

= (100/4)

= 25%

(ii) According to the question required percentage = (10/125) × 100

= (1000/125)

= 8%

(iii) According to the question required percentage = (160/4) × 100

We know that 1km = 1000 meters

Therefore 4km = 4000 meters

= (160/4000) × 100

= 4%

(iv) According to the question required percentage = (25/8) × 100

We know that 1Rs = 100 paise

Therefore 8Rs = 800 paise

= (25/800) × 100

= (25/8)

= 3.125%

(v) We know that 1day = 24 hours

1 hour = (1/24) day

8 hours = (8/24) day = (1/3) day

According to the question required percentage = (1/3)/2 × 100

= 100/6

= 16 (2/3) %

(vi) We know that 1liter = 1000ml

According to the question required percentage = (175/1000) × 100

= 17500/1000

= 17.50 %

Let the required number be x

Given that 50 % of x = 6

(50/100) × x = 6

x = (300 × 2)/ 50

x = 12

The required number is 12.

Let the required number be x

Then according to the question, 6 ¼ % × x = 64

= 6.25 % × x = 2

= (6.25/100) × x = 2

x = (2 × 100)/ 6.25

x = 2 × 16 = 32

Therefore 32 is the number whose 12 ½ % is 64.

Let the required number be x

Then according to the question, 12 ½ % × x = 64

= 12.5 % × x = 64

= (12.5 × 100) × x = 64

x = (64/100)/ 12.5

x = 64 × 8 = 512

Therefore 512 is the number whose 12 ½ % is 64.

Goods taxable at 5% turover = Rs. 50,000 

Tax = 50% of Rs.50,000 = Rs. 2,500 

of goods taxable at 125, turover = Rs. 3,20,000 

tax = 12% of Rs.3,20,000 = Rs.38,400 

Given tax exampled sales = Rs.45,000 

Total tax = Rs. 2,500 + Rs. 38,400 = Rs. 40,900 

Tax paid = Rs. 38,000 ‘ 

Net tax payable = Total tax changed – tax paid 

= Rs. 40,900 – Rs. 38,000 = Rs.2,900 

∴ Tax liability (under VAT) = Rs. 2,900

(i) Let the price of the commodity for the manufacture be Rs. x, tax is 10%. 

∴ tax charged by the manufactures = 10% of C.P

= 10x/100  10x/100

x + 10x/100 = 22, 000

⇒ x = (22000 x 100)/110 = 20,000

∴ The sale price of the commodity for the manufacture = 20,000 

(ii) VAT collected by the manufacture = tax charged by the manufacture

= 10x/100 = (10 x 20000)/100 = 2, 000 = tax paid by the distributor

since the distributor has sold the commodity tot he retailer for Rs.22,000 

∴ tax collected by the distributor = 10% of 22,000 

= 10/100 × 22000 = Rs.2200 = paid by retailer 

VAT to be deposited by the distributor = Rs.2200 – Rs.2000 = Rs.200

Tax collected by retailer = 10% of 25000 

= 10/100 × 25,000 = ‘2500 

∴ VAT to be paid by the retailer = Rs.2500 – Rs.2200 = Rs.300 

∴ Amount of the (under VAT) received by the state government 

= Rs.2000 + Rs.200 + Rs.300 = Rs.2500

[3(1/3)] % of 90 km

We have,

= (10/3) % of 90 km

= [(10/3) × (1/100)] × 90

= (1/30) × 90

= (1/1) × 3

= 3 km

Let the total number of examines = Z 

Percentage of examines failed = (100 – 65) % = 35% 

∴ 35% of Z = 420 

⇒ Z × 35/100 = 420 

⇒ Z = 420 × 100/35 

⇒ Z = 12 × 100 

⇒ Z = 1200

Let the number of apple trees be x

Number of trees in the orchard = 240

Number of apple trees = 16 (2/3) %

According to the given condition, 16 (2/3) % of 240 = x

= 16.66 % of 240 = x

x = (16.66/100) × 240

x = 40 trees

Number of other types of trees = Total number of trees – number of apple trees

= 240 – 40

= 200 trees

Given marks scored by Ram = 553/700

Percentage of marks scored by Ram = (553/700) × 100

= 0.79 × 100 = 79%

Also given that marks scored by Gita = (486/600)

Percentage of marks scored by Gita = (486/600) × 100

= 0.81 × 100 = 81

Gita’s performance (81%) is better than Ram’s (79%).

4 hours 30 min = (4 × 60) + 30 

= 240 + 30 

= 270 min 

24 hours = 24 × 60 

= 1440 min 

Now, 

Percentage = (270/1440 × 100) % 

= (3/16 × 100) % 

= (3/4 × 25) % 

= (75/4) %

= \(18\frac{3}{4}\%\)

2.8 % of 35

The above question can be written as,

= (2.8/ 100) × 35

= (28/1000) × 35

= (28/200) × 7

= (196/200)

= 0.98

Given Nazima’s total income = Rs 15000

Amount Nazima spends = Rs 10200

Amount Nazima saves = 15000 – 10200

= Rs 4800

Percentage of income Nazima saves = (4800/10200) × 100

= 480000/10200

= 32%

Nazima saves 32% of her income.

We need to convert liters into ml by multiplying by 1000 we get,

2l= 2 × 1000 = 2000ml

Now, calculating the percentage

(250/2000 × 100) %

(250/20) % = 12.5 %

The given details are,

Percentage Rohit deposited in bank = 12% of total income

Rohit deposited money during the year 1997 = Rs 1440

So, let us consider the total income of Rohit as Rs x

By calculating,

(x/100) × 12 = 1440

By cross multiplying

x = (1440×100)/22

= 12000

∴ Rohit’s total income for the year 1997 is Rs 12000.

Given total number of students who appeared for the examination = 1650

Number of students who failed = 8% of 1650   

= (8/100) ×1650

= (8 × 1650)/100

= 13200/100

Number of students who failed = 132 

Number of students who passed = 1650 – 132

= 1518

Percentage of students who passed = (1518/1650) × 100

= 0.92 × 100 = 92%

92% of the students passed the examination. 

Given total number of students in the school = 880

Number of boys in the school = 45% of 880

= (45/100) × 880

= 39600/100

Number of boys = 396

Number of girls in the school = total number of students – number of boys

= 880 – 396

Number of girls = 484

105% means, 105 divided by 100. 

So, 105% = 105/100 

= 1.05

[1(3/5)]

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= [1(3/5)] × 100

= (8/5) × 100

= (8 × 20)

= 160 %

(2/3)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (2/3) × 100

= (200/3)

= 66(2/3) %

(4/15)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (4/15) × 100

= (4/3) × 20

= 26(2/3) %

(19/500)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (19/500) × 100

= (19/5)

= 3.8%

First we convert the ratio into fraction 4:5 = 4/5

Now the number has to be multiplied by 100 we get, ((4/5) × 100) % = 80%

4 : 5 = \(\frac{4}{5}\)

= \((\frac{4}{5}\times100)\) % [Because 100% = 1]

= 80%

(8/125)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (8/125) × 100

= (8/5) × 4

= (32/5)

= 37(1/2) %

Given total number of marks = 80

Marks scored by Rohit = 45

Percentage obtained by Rohit = (45/80) × 100

= 56.25%

Given that total number of eggs = 60

Number of eggs rotten = 16 (2/3) % of 60 eggs

= 16.66 % of 60 eggs

= (16.66/100) × 60

= 10 eggs

Therefore number of eggs rotten = 10

From the question,

Monthly salary of typist is = ₹ 15625

The percentage of increase in his salary = 12%

Amount increase = 12% of ₹ 15625

= (12/100) × 15625

= (0.12 × 15625)

= ₹ 1875

∴his new salary = ₹ 15625 + ₹ 1875

= ₹ 1750

From the question,

The original excise duty on a certain item = ₹ 950

The reduced excise duty on a certain item = ₹ 760

The total amount reduced = (950 – 760)

= ₹ 190

Percentage of reduction = (reduced amount/original amount) × 100

= (190/950) × 100

= (19/95) × 100

= 20%

Hence, the percentage reduction in excise duty on a certain item is 20%

Total region = 4 parts 

Shaded region = 1 part 

Fraction of shaded region = \(\frac{1}{4}\)

Percentage of shaded region = \(\frac{1}{4}\) x \(\frac{100}{100}\)

= \(\frac{1}{4}\) x 100 %

= 25 %

(i) 1.425

142.5 % = \(\frac{1425}{10}\) % 

= \(\frac{1425}{10}\) x \(\frac{1}{100}\)

= 1.425

(iii) 0.5 %

0.005 = \(\frac{5}{1000}\)

= \(\frac{5}{1000}\) x \(\frac{100}{100}\)

= 0.5 %

 [16(2/3)] % of 16

The above question can be written as,

= (50/3) % of 16

= [(50/3) / (100)] × 16

= [(50/3) × (1/100)] × 16

= (1/6) × 16

= (8/3)

= [2(2/3)]

136 % of 70

The above question can be written as,

= (136 / 100) × 70

= (136/10) × 7

= (952/10)

= 95.2

(3) 133 (1/3)%

Let us consider a number x

So, x% of 90 is 120

x% × 90 = 120 x/100 × 90 = 120

90x = 120 × 100

x = 12000/90 = 133 (1/3)%

0.6

Multiply the given decimal by 100 and put the percent sign %.

We have,

= (0.6 × 100)

= 60%

5: 4

First convert the given ratio into fraction, and then multiply the fraction by 100 and put the percent sign %.

= (5/4)

= (5/4) × 100

= (5× 25)

= 125 %

 0.42

Multiply the given decimal by 100 and put the percent sign %.

We have,

= (0.42 × 100)

= 42%

0.07

Multiply the given decimal by 100 and put the percent sign %.

We have,

= (0.07 × 100)

= 7%

(4) 2.5%

We need to convert kg into grams by multiplying by 1000 we get,

10 kg= 10 × 1000 = 10000 g

Now, let us consider a number xx% of 10000 is 250

x% × 10000 = 250

100x = 250

x = 250/100 = 2.5%

(3/8)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (3/8) × 100

= (3/2) × 25

= (75/2)

= 37.5%

(9/20)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (9/20) × 100

= 9 × 5

= 45%

0.005

Multiply the given decimal by 100 and put the percent sign %.

We have,

= (0.005 × 100)

= 0.5%

Let, Z% of 400 = 600 

⇒ Z/100 × 400 = 60 

⇒ 4 Z = 60 

⇒ Z = 60/4 

⇒ Z = 15

6.5 % of 400

The above question can be written as,

= (6.5 / 100) × 400

= (65/1000) × 400

= (65/10) × 4

= (260/10)

= 26

(2) 600

Let us consider a number x

40% of x = 24040/100 × x = 240

x = 240 × 100/40

x = 600

(47/100)

In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.

= (47/100) × 100

= 47%