Chapter-8 Comparing quantities

Explanation:

To find the ratio of Rs 5 to 50 paise

First Convert paise to rupees. We know that 100 paise makes 1 rupee. So, we can convert 50 paise to rupees as follows:

50 paise = 50/100 rupees

= Rs 0.50

The ratio of Rs 5 to 50 paise can be written as

5:0.50

We can simplify the ratio by dividing both sides by 0.50:

5/0.50:0.50/0.50

10:1

Therefore, the ratio of 25 to 50 paise is 10:1

Explanation:

To compare 15 kg and 210 g, we need to convert them to the same unit. 1 kg is equal to 1000 g so we can convert 15 kg to grams as follows

15 kg = 15 x 1000 g

= 15,000 g

Now, we can write down the numbers in the ratio format:

15000: 210

We can simplify the ratio by dividing both sides by 30:

Therefore, 15000: 210=500:7

Explanation:

To compare 9 m and 27 cm. we need to convert them to the same unit. I m is equal to 100 cm, so we can convert 9m to centimeters as follows:

9m=9x 100 cm

=900 cm

Now, we can write down the numbers in the ratio format:

900: 27

We can simplify the ratio by dividing both sides by 27:

900/27:27/27 =100:3

Explanation:

To compare 30 days and 36 hours, we need to convert them to the same unit. 1 day is equal to 24 hours, so we can convert 30 days to hours as follows:

30 days = 30 x 24 hours

= 720 hours

Now, we can write down the numbers in the ratio format:

720:36

We can simplify the ratio by dividing both sides by 36:

720/36:36/36

20:1

Therefore, the ratio of 30 days to 36 hours is 20: 1.

Explanation: 

We can start by using the given ratio of computers to students to find out how many computers are needed per student:

3 computers: 6 students

To find out how many computers are needed per student, we can simplify the ratio by dividing both sides by 3:

1 computer: 2 students

This means that for every 2 students, a computer is needed.

To find out how many computers are needed for 24 students, we can set up a proportion:

1 computer / 2 students = x computers / 24 student where x is the number of computers needed for 24 students.

To solve for x, we can cross-multiply:

2x x=1 x 24

2x=24

X=12

Therefore, 12 computers are needed for 24 students in the computer lab.

Explanation:

(i) To find the population density of each state, we need to divide the population of each state by its corresponding area

For Rajasthan:

Population density = Population/Area

=570 lakhs / 3 lakh km²

= 190 people/km²

For UP:

Population density = Population / Area

= 1660 lakhs / 2 lakh km²

= 830 people/km²

(ii) Comparing the population densities of both states, we see that Rajasthan has a population density of 190 people/km and UP has a population density of 830 people/km². Therefore, Rajasthan is less populated than UP. 

Explanation:

To convert 1/8 to a percentage, we can use the following formula:

Percentage = (Fractional value) x 100%

Substituting the given value, we get:

Percentage (1/8) x 100%

= 12.5%

Therefore, 1/8 is equivalent to 12.5% as a percentage.

Explanation:

To convert 5/4 to a percentage, we can use the following formula:

Percentage (Fractional value) x 100%

Substituting the given value, we get:

Percentage = (5/4) x 100%

=125%

Therefore, 5/4 is equivalent to 125% as a percentage. 

Explanation:

To convert 3/40 to a percentage, we can use the following formula:

Percentage = (Fractional value) x 100%

Substituting the given value, we get:

Percentage (3/40) x 100%

=7.5%

Therefore, 340 is equivalent to 7.5% as a percentage.

Question 10. 2/7

Explanation:

To convert 2/7 to a percentage, we can use the following formula:

Percentage (Fractional value) x 100%

Substituting the given value, we get:

Percentage = (2/7) x 100%

=28.57%

Therefore, 2/7 is equivalent to 28.57% as a percentage.

Convert the given decimal fraction to percent.

Explanation:

First of all to convert it to a whole number hy multiplying numerator and denominator from 100 (0.65 x 100)/100=65/100

Simplify the fraction by dividing both the numerator and denominator by their HCF In this case, the HCF of 65 and 100 is 5.

we get. 13/20

So, we can simplify 65/100 by dividing both by 5

Convert the simplified fraction to a percentage by multiplying by 100, 13/20 x 100 = 65%

Therefore, 0.65 is equivalent to 65% as a percentage.

Explanation:

First of all Multiply 2.1 by 100 to get the fraction form.

2.1 x 100 = 210/100

Simplify the fraction by dividing both the numerator and denominator by their HCF

In this case, the HCF of 210 and 100 is 10.

210/10-21

100/10 = 10

So, 210/100 can be simplified to 21/10.

Convert the simplified fraction to a percentage by multiplying by 100.

21/10 x 100 = 210%

Therefore, 2.1 is equivalent to 210% as a percentage.

Explanation:

First of all Multiply 002 by 100 to make it a whole number.

0.02 x 100 = 2

Simplify the fraction by dividing both the numerator and denominator by their HCF.

In this case, the HCF of 2 and 100 is 2.

So, we can simplify 2/100 by dividing both by 2. We get 1/50.

Convert the simplified fraction to a percentage by multiplying by 100.

1/50 x 1XI=2%

Therefore, 0012 is equivalent to 25% as a percentage.

Explanation:

First of all Multiply 12.35 by 100 to get a whole number.

12.35 x 100=1235

Simplify the whole number by dividing both the numerator and denominator by their HCF. In this case, the HCF of 1235 and 100 is 5.

1235/5=247

100/5=20

Convert the simplified fraction to a percentage by multiplying by 100,

247/20 x 100 = 1235%

Explanation:

To find the percentage of the figure that is colored, we can divide the number of colored parts (1) by the total number of parts (4), and then multiply by 100 to get the percentage:

Percentage = (Number of colored parts/Total number of parts) x 100%

Substituting the given values, we get

Percentage = (1/4) x 100%

=25%

Therefore, 25% of the figure is colored.

13/45

Explanation:

To find the percentage of the figure that is colored, we can use the following formula:

Percentage = (Number of colored parts/Total number of parts) x 100%

Substituting the given values, we get:

Percentage (375) x 100%

=60%

Therefore, 60% of the figure is colored

Explanation:

To find the percentage of the figure that is colored, we can use the following formula:

x=14+0.7

Simplifying, we get:

x=20

Therefore, the whole quantity is 20 minutes.

Explanation:

Rewrite 8% as a fraction

8%= 8/100

Let's assume the whole quantity as 'x

Then, we can write the following equation to represent the given information:

8/100x40

Simplify the equation by dividing both sides by 8/100

x=40+(8/100)

x=40+0.08

Calculate the value of x

x = 500

Therefore, the whole quantity is 500 liters.

Explanation:

To convert 25% to a decimal fraction, we simply divide 25 by 100:

25÷100=0.25

So, 25% as a decimal fraction is 0.25.

To convert 25% to a fraction, we can write:

25%= 25/100

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25:1

25/100= (25+25)/(100+25)=1/4

Therefore, 25% as a fraction in simplest form is 1/4.

Explanation:

To convert 150% to a decimal fraction, we divide it by 100:

150% 100% 15

So, 150% is equivalent so the decimal fraction 15.

To convert 150% to a fraction in simplest form, we can first write it as a fraction with a denominator of 100:

150%=150/100

Then, we can simplify the fraction by dividing both the numerator and denominator by their

greatest common factor, which is 50:

150/100=(150+50(100-50)=3/2

Explanation:

To convert 20% to a decimal fraction, we divide it by 100:

20%-100% = 0.2

So, 20% is equivalent to the decimal fraction 0.2.

To convert 20% to a fraction in simplest form, we can write it as a fraction with a denominator of 100

20%= 20/100

Then, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 20.

20/100 = (20+201/(100+20)=1/5

Therefore, 20% is equivalent to the decimal fraction 0.2 and the fraction 1/5 in simplest form

Explanation:

To convert 5% to a decimal fraction, we divide it by 100:

5%-100% = 0.05

So, 5% is equivalent to the decimal fraction 0:05.

To convert 5% to a fraction in samplest form, we can write it as a fraction with a denominator of 100

5%= 5/100

Then, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5:

5/100=5+5)/(100+5)=1/20

Therefore, 5% is equivalent to the decimal fraction 0.05 and the fraction 1/20 in simplest form.

Explanation:

According to the question, in a city

Female percentage=3%

Male percentage = 40%

Let children's percentage be x

Then,

City comprises of (% of Male +% of Female +% of Children) = ( 30% +40%+x%)

Therefore, 100% of population (% of Male + % of Female + % of Children)

We can write it as

(30% +40% + x%) = 100%

x%= 100% - 30% +40%)

x=30%

So, The childrens are 30%

Explanation:

According to the question:

Out of 15000 voters in the constituency, 60% voted. This means that:

Number of voters who voted = 60% of 15,000

=(60/100) x 15:000

=9000

To find the percentage of voters who did not vote, we can subtract the percentage of voters who voted from 100%

Percentage of voters who did not vote 100%-60%

=40

So, 40% of the voters in the constituency did not vote.

voters:

To find the actual number of voters who did not vote, we can calculate 40% of the total number of 15000

Number of voters who did not vote 40% of 15000

=(40/100) x 15000

6,000

Therefore, 6000 voters in the constituency did not vote.

Explanation:

Let his salary be x. then according to question:

Meeta saves 10% of her salary of which is  4000 do this by dividing both sides of the equation in step 1 by 10%.

To find Mecta's salary, we need to figure out what amount represents 100% of her salary. We can

10% of salary (x)-4000

1% of salary (x) = 4000-10-7400

100% of salary (x) 100x400-240,000

Therefore, Meeta's salary is ₹ 40,000

Explanation:

To find out how many matches the cricket team won, we can multiply the total number of matches played by the percentage of matches won

Number of matches won = 25% of 20 matches

We can convert 25% to a decimal by dividing it by 100-

25% +1(K)=0.25

Substituting this value, we get:

Number of matches won=0.25 x 20

Therefore, the cricket tearn won 5 matches.

Explanation:

Profit=Selling Price-Cost Price

Loss - Cost Price - Selling Price

Profit Percentage = (Profit / Cost Price) x 100

Loss Percentage = (Low/Cost Price) x 100

In this case, the gardening shears were bought for 250 and sold for 325.

Cost Price (CP)=250

Selling Price (SP)= 325

Now, let's calculate the profit or loss:

Profit=SP-CP=325-250=75

Since the value of profit is positive, this means, there is a profit.

Now, let's calculate the profit percentage:

Profit Percentage (Profit/CP) x 100 =(75/250) x 100

30%

Therefore, the profit in this transaction is 75 and the profit percentage is 30%

Explanation:

Profit Selling Price-Cost Price

Loss = Cost Price - Selling Price

Profit Percentage = (Profit / Cost Price) x 100 Loss Percentage = (Loss / Cost Price) x 100

In this case, the refrigerator was bought for 12,000 and sold for 13,500.

Cost Price (CP) - 12,000 Selling Price (SP)- 13,500

Now, let's calculate the profit or loss:

Profit=SP-CP-13,500 - €12,000 - 1,500

Since the value of profit is positive, this means there is a profit.

Now, let's calculate the profit percentage:

Profit Percentage = (Profit/CP) x 100

= (1500/12000) x 100

= 12.5%

Therefore, the profit in this transaction is 1,500 and the profit percentage is 12.9%

Explanation:

Profit = Selling Price - Cost Price

Loss of Cost Price - Selling Price

Profit Percentage = (Profit/Cost Price) x 100 Loss Percentage = (Low Cost Price) x 100

In this case, the cupboard was bought for 2,500 and sold for 23,000.

So,

Cost Price(CP)=2,500

Selling Price (SP) =3,000

Now, let's calculate the profit or loss:

Profit=SP-CP=

3,000 - 2,500

= 500

Since the value of profit is positive, this means there is a profit.

Now, let's calculate the profit percentage:

Profit Percentage (Profit/CP) x 100

= (500/2500) x 100

=20%

Therefore, the profit in titis transaction is 500 and the profit percentage is 20%

Explanation:

Profit-Selling Price - Cost Price

Loss = Cost Price - Selling Price

Profit Percentage = (Profit/Cost Price) x 100

Loss Percentage = (Loss/Cost Price) x 100

In this case, the skirt was bought for 250 and sold for 150,

Cost Price (CP)= 250.

Selling Price (SP) = 150

Now, let's calculate the profit or loss:

Loss =CP-SP=250-150=100

Since the value of loss is positive, this means there is a loss.

Now, let's calculate the loss percentage:

Loss Percentage = (Loss/CP) x 100

= (100/250) x 100

40%

Therefore, the loss in this transaction is 100 and the loss percentage is 40%

Explanation:

To convert a ratio to a percentage, we need to add the two parts of the ratio and then express each part as a percentage of the total.

In this case, the ratin is 3:1.

So, the total parts in the ratio 3+1 4.

Now, let's convert each part to a percentage:

First part 3/4 x 100% = 75%

Second part = 1/4 x 100% = 25%

Therefore, part of 3:1 can be expressed as 75% and 25%

Explanation:

To convert a ratio to a percentage, we need to add the three parts of the ratio and then express each part as a percentage of the total.

In this case, the ratio is 2-3:5

So, the total parts in the ratio = 2+3+5-10

Now, let's convert each part to a percentage:

First part 2/10 x 100% = 20%

Second part = 3/10 x 100% = 30% Third part = 5/10 x 100% = 50%

Therefore, the part of 2-1-5 can be expressed as 20%, 30% and 50%.

Explanation:

To convert a ratio to a percentage, we need to add the two parts of the ratio and then express each part as a percentage of the total.

In this case, the ratio is 154.

So, the total parts in the ratio=1+4=5.

Now, let's convert each part to a percentage:

First part = 1/5 x 100%-20%

Second part = 4/5 x 100% = 80%

Therefore, the part of 1:4 can be expressed as 20% and 80%.

Explanation:

To convert a ratio to a percentage, we need to add the three parts of the ratio and then express each part as a percentage of the total

In this case, the ratio is 1:2:5

So, the total parts in the ratio=1+2+5-8

Now, let's convert each part to a percentage:

First part 1/8 x 100% 12.5%

Second part = 2/8 x 100% = 25%

Third part 5/8 x 100% 62.5%

Therefore, the part of 1-2-5 can be expressed as 12.5% 25% and 62.5%

Explanation:

To find the percentage decrease, we need to calculate the decrease in population and then express it us a percentage of the original population

In this case, the original population was 25,000 and it decreased to 24.500.

So, the decrease in population = 25.000 -24,500 = 500

Now, let's calculate the percentage decrease:

Percentage Decrease = (Decrease in population/Original population) x 100% = (500/25000) x 100%

=2%

Therefore, the percentage decrease in population is 2%.

Explanation:

To find the percentage increase, we need to calculate the increase in price and then express it as a percentage of the original price.

In this case. Arun bought a car for 350,000 and the price increased t ed to 3,70,000.

So, the increase in price =

3,70,000-3,50,000

Now, let's calculate the percentage increases

= 20,000.

Percentage Increase = (Increase in price / Original price) x 100% (203000/350,000) x 100%

=40/7

5.71% (approx)

Therefore, the percentage increase in price is 40/7 or approximately 5.71%,

Explanation:

According to the question a TV is bought for 10,000 and sold at a profit of 20%. Cost price of TV = 10,000)

Profit = 20%

The selling price is calculated us:

Selling price = Cost price - Profit - 10,000+20% of 10,000

= 10,000+ 2,000

=12,000 So, at 20% of profit. The selling price of TV is 12,000

Explanation:

If Juhi sold a washing machine for 13,500 and suffered a loss of 20%, then the selling price would be 80% of the cost price.

Let's assume the cost price of the washing machine to be CP.

Then, selling price (SP)-13,500) Loss percentage (1%) = 20%

Profit percentage (PS) = 0% (as she suffered  loss)

We know that:

Selling price - Cost price x (100% - Loss %) / 100% or, SP=CP x (100% -1%) / 100%

Substituting the given values, we get:

13.500 =CP x(100% -20%)/100

13,500=CP x 80 / 100

13,500=4CP/5

CP=( 15,500 x 5) 4

CP=16,875

Therefore, the cost price of the washing machine was € 16,875.

Explanation:

The ratio of calcium, carbon, and oxygen in chalk is 10:3:12

Therefore, the total ratio of the components in chalk is 10-3+12=25.

To find the percentage of carbon in chilk, we need to first calculate the fraction of carbon in the total ratio:

Fraction of carbon=3/25

Now, let's convert this fraction into a percentage:

Percentage of carbon = (Fraction of carbon) x 100%

= (3/25) x 100%

= 12%

Therefore, the percentage of carbon in chalk is 12%

Explanation:

If in a stick of chalk, the weight of carbon is 3g and the ratio of calcium, carbon, and oxygen in chalk is 10:3:12, then we can find the weight of the entire chalk stick as follows:

Let the weight of the entire chalk stick be x.

The ratio of carbon to the total components in chalk is 3:25.

So, the fraction of the weight of the carbon to the weight of the entire chalk suck is 3/25

Therefore, we can write the following equation:

3/25=3/x

Solving for x, we get:

x=(25 x 3)/3

X=25

Therefore, the weight of the chalk stick is 25g.

Explanation:

Given, the cost price of the book is 275 and the loss incurred is 15%.

So, the loss incurred by Amina

=15% of 275

=(15/100) 275

=41.25

Now, we can find the selling price of the book by subtracting the loss from the cost price:

Selling price = Cost price - Loss

=8275-341.25

=233.75

Therefore, Amina sells the book for 233.75 after incurring a loss of 15%

Explanation:

Simple Interest = (P xR x T)/100

Where.

P=Principal amount

R=Rate of interest per annum

T = Time period in years

Given,

Principal (P)=1.200

Rate of interest (R) = 12% pa.

Time period (T) = 3 years

Substituting the values in the formula, we get:\

39/45

Simple Interest = (1200x12x3)/100 -3432

Amount to be paid =Principal + Simple Interest

=1,200+.432

=1.632

Therefore, the amount to be paid at the end of 3 years, when the principal is ₹ 1,200 at 12% pa. is 1.632.

Explanation:

Simple Interest (PxRxT)/100

Where.

P=Principal amount

R=Rate of interest per annum

T-Time period in years

Given

Principal (P)-7,500)

Rate of interest (R)-5% pa.

Time period (T) = 3 years

Substituting the values in the formula, we get:

Simple Interest = (7,500 × 5x3)/100

=31,125

Amount to be paid Principal + Simple Interest

=7,500+ 1,125

=28,625

Therefore, the amount to be paid at the end of 3 years, when the principal is 7,500 at 5% pa. is 28,625.

Explanation:

Simple Interest (P x R x T)/100

Where,

P = Principal amount

R=Rate of interest per annum

T=Time period in year

Given.

Principal (1) - 56,000

Time period (T) = 2 years Simple Interest - 280

Substituting the given values in the formula, we get:

280= (56,000 x R x 2)/100

Simplifying the above expression, we get

28000 = 56:000 * R

R=28000/36,000

R=0.5 or 50%

Therefore, the rate of interest that gives 280 as interest on a sum of 56,000 in 2 years is 50%.

Explanation:

Simple Interest = (PRT)/100

Where.

P=Principal amount R=Rate of interest per annum

T = Time period in years

Given,

Simple Interest = 45

Rate of interest (R)=9% pa. Time period (T) = 1 year

Substituting the given values in the formula, we get:

45 = (P x 9x1)/100

Simplifying the above expression, we get:

P = (45×100)/9

P=2500

Therefore, the sum that Meena has borrowed is 2500.