**Exercise 8.1**

**1.Find the ratio of:**

(a) Rs. 5 to 50 paise

(b) 15 kg to 210 g

(c) 9 m to 27 cm

(d) 30 days to 36 hours

Solution:

(a) Rs. 5 to 50 paise

Converting the given quantities into same units, we have

Rs. 5 = 5 × 100 = 500 paise

∴ Rs. 5 : 50 paise

= 500 paise : 50 paise [∵ Rs. 1 = 100 paise]

= 10 : 1

So, required ratio is 10 : 1.

(b) 15 kg to 210 g

Converting the given quantities into same units, we have

15 kg = 15 × 1000

= 15000 g [∵ 1 kg = 1000 g]

∴ 15 kg : 210 g = 15000 g : 210 g

= 1500 : 21

= 500 : 7

So, the required ratio is 500 : 7.

(c) 9 m to 27 cm

Converting the given quantities into same units, we have

9 m = 9 × 100 = 900 cm

∴ 9m: 27 cm = 900 cm : 27 cm [∵ 1 m = 100 cm]

= 100 : 3

So, the required ratio is 100 : 3.

(d) 30 days to 36 hours

Converting the given quantities into same

units, we have

30 days = 30 × 24 hours [ ∵ 1 day = 24 hours]

= 720 hours

∴ 30 days : 36 hours

= 720 hours : 36 hours = 20:1

So, the required ratio is 20 : 1.

**2. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?**

**Solution:-**

From the question it is given that,

Number of computer required for 6 students = 3

So, number of computer required for 1 student = (3/6)

= ½

So, number of computer required for 24 students = 24 × ½

= 24/2

= 12

∴Number of computer required for 24 students is 12 computers.

**3. Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.**

**Area of Rajasthan = 3 lakh km ^{2} and area of UP = 2 lakh km^{2}.**

**(i) How many people are there per km ^{2} in both these States?**

**(ii) Which State is less populated?**

**Solution:-**

(i) From the question, it is given that,

Population of Rajasthan = 570 lakh

Area of Rajasthan = 3 lakh Km^{2}

Then, population of Rajasthan in 1 km^{2} area = (570 lakh)/ (3 lakh km^{2})

= 190 people per km^{2}

Population of UP = 1660 Lakh

Area of UP = 2 Lakh km^{2}

Then, population of UP in 1 lakh km^{2} area = (1660 lakh)/ (2 lakh km^{2})

= 830 people per km^{2}

(ii) By comparing the two states Rajasthan is the less populated state.

**Exercise 8.2**

**1. Convert the given fractional numbers to percent.**

**(a) 1/8**

**Solution:-**

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

= (1/8) × 100 %

= 100/8 %

= 12.5%

**(b) 5/4**

**Solution:-**

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

= (5/4) × 100 %

= 500/4 %

= 125%

**(c) 3/40**

**Solution:-**

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

= (3/40) × 100 %

= 300/40 %

= 30/4 %

= 7.5%

**(d) 2/7**

**Solution:-**

= (2/7) × 100 %

= 200/7 %

**2. Convert the given decimal fraction to percent.**

**(a) 0.65**

**Solution:-**

First we have to remove the decimal point,

= 65/100

Now,

Multiply by 100 and put the percent sign %.

We have,

= (65/100) × 100

= 65%

**(b) 2.1**

**Solution:-**

First we have to remove the decimal point,

= 21/10

Now,

Multiply by 100 and put the percent sign %.

We have,

= (21/10) × 100

=210%

**(c) 0.02**

**Solution:-**

First we have to remove the decimal point,

= 2/100

Now,

Multiply 100 and put the percent sign %.

We have,

= (2/100) × 100

= 2%

**(d) 12.35**

**Solution:-**

First we have to remove the decimal point,

= 1235/100

Now,

Multiply by 100 and put the percent sign %.

We have,

= (1235/100) × 100)

= 1235%

**3. Estimate what part of the figures is coloured and hence find the per cent which is coloured.**

**Solution:-**

**(i)**

By observing the given figure,

We can able to identify that 1 part is shaded out of 4 equal parts.

It is represented by a fraction = ¼

Then,

= ¼ × 100

= 100/4

= 25%

Hence, 25% of figure is coloured.

**(ii)**

By observing the given figure,

We can able to identify that 3 part is shaded out of 5 equal parts.

It is represented by a fraction = 3/5

Then,

= (3/5) × 100

= 300/5

= 60%

Hence, 60% of figure is coloured.

**(iii)**

By observing the given figure,

We can able to identify that 3 part is shaded out of 8 equal parts.

It is represented by a fraction = 3/8

Then,

= (3/8) × 100

= 300/8

= 37.5%

Hence, 37.5% of figure is coloured.

**4. Find:**

**(a) 15% of 250**

**Solution:-**

We have,

= (15/100) × 250

= (15/10) × 25

= (15/2) × 5

= (75/2)

= 37.5

**(b) 1% of 1 hour**

**Solution:-**

We know that, 1 hour = 60 minutes

Then,

1% of 60 minutes

1 minute = 60 seconds

60 minutes = 60 × 60 = 3600 seconds

Now,

1% of 3600 seconds

= (1/100) × 3600

= 1 × 36

= 36 seconds

**(c) 20% of Rs. 2500**

**Solution:-**

We have,

= (20/100) × 2500

= 20 × 25

= **Rs.** 500

**(d) 75% of 1 kg**

**Solution:-**

We know that, 1 kg = 1000 g

Then,

75% of 1000 g

= (75/100) × 1000

= 75 × 10

= 750 g

**5. Find the whole quantity if**

**(a) 5% of it is 600**

**Solution:-**

Let us assume the whole quantity be x,

Then,

(5/100) × (x) = 600

X = 600 × (100/5)

X = 60000/5

X = 12000

**(b) 12% of it is Rs. 1080.**

**Solution:-**

Let us assume the whole quantity be x,

Then,

(12/100) × (x) = 1080

X = 1080 × (100/12)

X = 540 × (100/6)

X = 90 × 100

X = Rs. 9000

**(c) 40% of it is 500k km**

**Solution:-**

Let us assume the whole quantity be x,

Then,

(40/100) × (x) = 500

X = 500 × (100/40)

X = 500 × (10/4)

X = 500 × 2.5

X = 1250 km

**(d) 70% of it is 14 minutes**

**Solution:-**

Let us assume the whole quantity be x,

Then,

(70/100) × (x) = 14

X = 14 × (100/70)

X = 14 × (10/7)

X = 20 minutes

**(e) 8% of it is 40 liters**

**Solution:-**

Let us assume the whole quantity be x,

Then,

(8/100) × (x) = 40

X = 40 × (100/8)

X = 40 × (100/8)

X = 40 × 12.5

X = 500 liters

**6. Convert given percent to decimal fractions and also fractions in simplest forms:**

**(a) 25%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (25/100)

= ¼

= 0.25

**(b) 150%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (150/100)

= 3/2

= 1.5

**(c) 20%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (20/100)

= 1/5

= 0.2

**(d) 5%**

**Solution:-**

First convert the given percentage into fraction and then put the fraction into decimal form.

= (5/100)

= 1/20

= 0.05

**7. In a city, 30% are females, 40% are males and remaining are children. What per cent are children?**

**Solution:-**

From the question, it is given that

Percentage of female in a city =30%

Percentage of male in a city = 40%

Total percentage of male and female both = 40% + 30%

= 70%

Now we have to find the percentage of children = 100 – 70

= 30%

So, 30% are children.

**8. Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?**

**Solution:-**

From the question, it is given that

Total number of voters in the constituency = 15000

Percentage of people who voted in the election = 60%

Percentage of people who did not voted in the election = 100 – 60

= 40%

Total number of voters who did not voted in the election = 40% of 15000

= (40/100) × 15000

= 0.4 × 15000

= 6000 voters

∴ 6000 voters did not vote.

**9. Meeta saves Rs. 4000 from her salary. If this is 10% of her salary. What is her salary?**

**Solution:-**

Let us assume Meeta’s salary be **Rs.** x,

Then,

10% of **Rs.** x = **Rs.** 4000

(10/100) × (x) = 4000

X = 4000 × (100/10)

X = 4000 × 10

X = **Rs.** 40000

∴ Meeta’s salary is **Rs.** 40000.

**10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?**

**Solution:-**

From the question, it is given that

Total matches played by a local team = 20

Percentage of matches won by the local team = 25%

Then,

Number of matches won by the team = 25% of 20

= (25/100) × 20

= 25/5

= 5 matches.

∴The local team won 5 matches out of 20 matches.

**Exercise 8.3**

**1. Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.**

**(a) Gardening shears bought for Rs.250 and sold for Rs. 325.**

**Solution:-**

From the question, it is given that

Cost price of gardening shears = **Rs.** 250

Selling price of gardening shears = **Rs. **325

Since (SP) > (CP), so there is a profit

Profit = (SP) – (CP)

= **Rs.** (325 – 250)

= **Rs.** 75

Profit % = {(Profit/CP) × 100}

= {(75/250) × 100}

= {7500/250}

= 750/25

= 30%

**(b) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.**

**Solution:-**

From the question, it is given that

Cost price of refrigerator = **Rs.** 12000

Selling price of refrigerator = **Rs.** 13500

Since (SP) > (CP), so there is a profit

Profit = (SP) – (CP)

= **Rs.** (13500 – 12000)

= **Rs.** 1500

Profit % = {(Profit/CP) × 100}

= {(1500/12000) × 100}

= {150000/12000}

= 150/12

= 12.5%

**(c) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.**

**Solution:-**

From the question, it is given that

Cost price of cupboard = **Rs.** 2500

Selling price of cupboard = **Rs.** 3000

Since (SP) > (CP), so there is a profit

Profit = (SP) – (CP)

= **Rs.** (3000 – 2500)

= **Rs.** 500

Profit % = {(Profit/CP) × 100}

= {(500/2500) × 100}

= {50000/2500}

= 500/25

= 20%

**(d) A skirt bought for Rs. 250 and sold at Rs. 150.**

**Solution:-**

Since (SP) < (CP), so there is a loss

Loss = (CP) – (SP)

= **Rs.** (250 – 150)

= **Rs.** 100

Loss % = {(Loss/CP) × 100}

= {(100/250) × 100}

= {10000/250}

= 40%

**2. Convert each part of the ratio to percentage:**

**(a) 3 : 1**

**Solution:-**

We have to find total parts by adding the given ratio = 3 + 1 = 4

1^{st} part = ¾ = (¾) × 100 %

= 3 × 25%

= 75%

2^{nd }part = ¼ = (¼) × 100%

= 1 × 25

= 25%

**(b) 2: 3: 5**

**Solution:-**

We have to find total parts by adding the given ratio = 2 + 3 + 5 = 10

1^{st} part = 2/10 = (2/10) × 100 %

= 2 × 10%

= 20%

2^{nd }part = 3/10 = (3/10) × 100%

= 3 × 10

= 30%

3^{rd }part = 5/10 = (5/10) × 100%

= 5 × 10

= 50%

**(c) 1:4**

**Solution:-**

We have to find total parts by adding the given ratio = 1 + 4 = 5

1^{st} part = (1/5) = (1/5) × 100 %

= 1 × 20%

= 20%

2^{nd }part = (4/5) = (4/5) × 100%

= 4 × 20

= 80%

**(d) 1: 2: 5**

**Solution:-**

We have to find total parts by adding the given ratio = 1 + 2 + 5 = 8

1^{st} part = 1/8 = (1/8) × 100 %

= (100/8) %

= 12.5%

2^{nd }part = 2/8 = (2/8) × 100%

= (200/8)

= 25%

3^{rd }part = 5/8 = (5/8) × 100%

= (500/8)

= 62.5%

**3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.**

**Solution:-**

From the question, it is given that

Initial population of the city = 25000

Final population of the city = 24500

Population decrease = Initial population – Final population

= 25000 – 24500

= 500

Then,

Percentage decrease in population = (population decrease/Initial population) × 100

= (500/25000) × 100

= (50000/25000)

= 50/25

= 2%

**4. Arun bought a car for Rs. 3,50,000. The next year, the price went upto Rs. 3,70,000. What was the Percentage of price increase?**

**Solution:-**

From the question, it is given that

Arun bought a car for = **Rs.** 350000

The price of the car in the next year, went up to = **Rs.** 370000

Then increase in price of car = **Rs.** 370000 – **Rs.** 350000

= **Rs.** 20000

The percentage of price increase = (**Rs.** 20000/ **Rs.** 350000) × 100

= (2/35) × 100

= 200/35

= 40/7

**5. I buy a T.V. for ₹ 10,000 and sell it at a profit of 20%. How much money do I get for it?**

**Solution:-**

From the question, it is given that

Cost price of the T.V. = Rs. 10000

Percentage of profit = 20%

Profit = (20/100) × 10000

= Rs. 2000

Then,

Selling price of the T.V. = cost price + profit

= 10000 + 2000

= Rs. 12000

∴ I will get it for Rs. 12000.

**6. Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What was the price at which she bought it?**

**Solution:-**

From the question, it is given that

Selling price of washing machine = Rs. 13500

Percentage of loss = 20%

Now, we have to find the cost price washing machine

By using the formula, we have:

CP = Rs. {(100/ (100 – loss %)) × SP}

= {(100/ (100 – 20)) × 13500}

= {(100/ 80) × 13500}

= {1350000/80}

= {135000/8}

= Rs. 16875

**7. (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.**

**Solution:-**

From the question it is given that,

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

So, total part = 10 + 3 + 12 = 25

In that total part amount of carbon = 3/25

Then,

Percentage of carbon = (3/25) × 100

= 3 × 4

= 12 %

**(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?**

**Solution:-**

From the question it is given that,

Weight of carbon in the chalk = 3g

Let us assume the weight of the stick be x

Then,

12% of x = 3

(12/100) × (x) = 3

X = 3 × (100/12)

X = 1 × (100/4)

X = 25g

∴The weight of the stick is 25g.

**8. Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it for?**

**Solution:-**

From the question, it is given that

Cost price of book = Rs. 275

Percentage of loss = 15%

Now, we have to find the selling price book,

By using the formula, we have:

SP = {((100 – loss %) /100) × CP)}

= {((100 – 15) /100) × 275)}

= {(85 /100) × 275}

= 23375/100

= Rs. 233.75

**9. Find the amount to be paid at the end of 3 years in each case:**

**(a) Principal = ₹ 1,200 at 12% p.a.**

**Solution:-**

Given: – Principal (P) = Rs. 1200, Rate (R) = 12% p.a. and Time (T) = 3years.

If interest is calculated uniformly on the original principal throughout the loan period, it is called Simple interest (SI).

SI = (P × R × T)/100

= (1200 × 12 × 3)/ 100

= (12 × 12 × 3)/ 1

= Rs.432

Amount = (principal + SI)

= (1200 + 432)

= Rs. 1632

**(b) Principal = ₹ 7,500 at 5% p.a.**

**Solution:-**

Given: – Principal (P) = Rs. 7500, Rate (R) = 5% p.a. and Time (T) = 3years.

If interest is calculated uniformly on the original principal throughout the loan period, it is called Simple interest (SI).

SI = (P × R × T)/100

= (7500 × 5 × 3)/ 100

= (75 × 5 × 3)/ 1

= Rs. 1125

Amount = (principal + SI)

= (7500 + 1125)

= Rs. 8625

**10. What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?**

**Solution:-**

Given: – P = Rs. 56000, SI = Rs. 280, t = 2 years.

We know that,

R = (100 × SI) / (P × T)

= (100 × 280)/ (56000 × 2)

= (1 × 28) / (56 × 2)

= (1 × 14) / (56 × 1)

= (1 × 1) / (4 × 1)

= (1/ 4)

= 0.25%

**11. If Meena gives an interest of Rs. 45 for one year at 9% rate p.a. What is the sum she has borrowed?**

**Solution:-**

From the question it is given that, SI = Rs. 45, R = 9%, T = 1 year, P =?

SI = (P × R × T)/100

45 = (P × 9 × 1)/ 100

P = (45 ×100)/ 9

= 5 × 100

= Rs. 500

Hence, she borrowed Rs. 500.