SEBA Class 7 Maths Chapter 8 Comparing Quantities Solutions | Exercises 8.1, 8.2 & 8.3 | Assam English Medium | SCERT Assam | QR Code: Y4L1X7

SEBA Class 7 Maths Chapter 8 Comparing Quantities Solutions | SCERT Assam | Exercises 8.1 to 8.3

Find SEBA Class 7 Maths Chapter 8 Comparing Quantities Solutions for Exercises 8.1, 8.2, and 8.3 in English Medium, following the SCERT Assam syllabus. This chapter covers essential concepts such as percentages, ratios, simple and compound interest, profit and loss, and discount calculations. Our step-by-step solutions make it easy for students to grasp these topics and apply them to real-life situations. Perfect for SEBA students preparing for exams. QR Code: Y4L1X7.

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Comparing Quantities

Exercise – 8.1

1. Find the ratios–

(i) 5 km and 500 m.

Ans: = 5 km/500 m

= 5 × 100 m/500 m

= 10/1

= 10:1

(ii) 6 week and 21 days.

Ans: 6 weeks/21 days

= 6 × 7 days/21 days

= 2/1

= 2:1

(iii) 30 days and 210 hours.

Ans: = 30 days/210 hours

= 30 × 24 hours/210 hours

= 24/7

= 24:7

(iv) 12 meter and 100 centimeter.

Ans: 12 m/100 centimeter

= 30 × 100 centimeter/100 centimeter

= 12/1

= 12:1

(v) 7 years and 18 months.

Ans: 7 years/18 months

= 12 × 12 months/18 months

= 12/1

= 12:1

2. Examine whether the following ratios are equivalent or not-

(i) 4:5 and 2:3

Ans: 4:5 and 2:3

4/5 = (4 × 3)/(5 × 3) = 12/15

2/3 = (2 × 5)/(3 × 5) = 10/15

∴ 4/5 > 2/3

∴ Not Equivalent.

(ii) 7:15 and 21:45

Ans: 7:15 and 21:45

7/15 = (7 × 3)/(15 × 3) = 21/45

21/45 = (21 × 1)(/45 × 1) = 21/45

∴ 7/15 = 21/45

∴ 7:15 and 21:45 are equivalent.

(iii) 6:8 and 54:72

Ans: 6:8 and 54:72

6/8 = (6 × 9)/(8 × 9) = 54/72

54/72 = (45 × 1)/(72 × 1) = 54/72

∴ 6/8 = 54/72

∴ 6:8 and 54:72 are equivalent.

(iv) 13:14 and 14:13

Ans: 13:14 and 14:13

13/14 = (13 × 13)/(14 × 13) = 169/182

14/13 = 14 × 14/13 × 14 = 196/182

13/14 ≠ 14/13 and 13/14<14/13

∴ 13:14 and 14:13 are not equivalent.

3. The price of three geometry boxes is 33. How many geometry boxes can be bought with 286?

Ans: Number of geometry boxes with Rs. 33 is 3

∴ Number of geometry boxes with Rs. 1 is 3/33

∴ Number of geometry boxes with Rs. 286 is

4. Kalpana has bought 10 balls with Rs. 160 and Jaymati has bought 8 balls with Rs. 128. Find if both of them have purchased at an equal price?

Ans: Number of balls has brought with Rs. 160 = 10

∴ Number of balls has brought with Rs. 1 = 10/160

= 1/16

= 1:16

Again, number of balls has brought with Rs. 128 = 8

∴ Number of balls has brought with Rs. 1 = 8/128

= 1/16

= 1:16

Again, They have purchased at an equal price.

5. Jenelia needs to pay 66,000/- as house rent for the whole year. If she wants to pay house rent every three months then how much will she need to pay each time?

Ans: For 12 months Jenelia needs to pay Rs. 66,000/- as a rent

∴ For 1 month Jenelia needs to pay Rs. 66,000/12 as house rent

∴ For 3 months Jenelia needs to pay Rs. 66,000/12 × 3 as house rent

= Rs. 16,500

Exercise – 8.2

1. Express the following fraction in percentage–

(i) 3/5

Ans: 3/5 × 100%

= 3 × 20%

= 60%

(ii) 7/12

Ans: 7/12 × 100%

= 175/3% = 58.33%

(iii) 15/32

Ans: 15/32 × 100%

= 375/8%

= 46.88%

(iv) 91/175

Ans:

(v) 21/40

Ans: 21/40 × 100%

= 105/2%

= 52.5%

2. Express the decimal fraction in percentage–

(i) 0.8

Ans: 0.8 × 100%

= 8/10 × 100%

= 80%

(ii) 5.75

Ans: 5.75 × 100%

= 575/100 × 100%

= 575%

(iii) 0.08

Ans: 0.08 × 100%

= 8/100 × 100%

= 8%

(iv) 32.1

Ans: 32.1 × 100%

= 321/10 × 100%

= 3210%

(v) 0.004

Ans: 0.004 × 100%

= 4/4000 × 100%

= 4/10%

= 0.4%

3. Express in fraction–

(i) 20%

Ans: 20%

= 20/100

= 1/5

(ii) 32%

Ans: 32%

= 32/100

= 8/25

(iii) 0.5%

Ans: 0.5%

= 5/100

= 5/10 × 100

= 1/200

(iv) 7.25%

Ans: 7.25%

= 725/100 × 100

= 29/400

(v) 180%

Ans: 180%

= 180/100

= 1 4/5

4. Convert the percentages into decimal fraction and express the fraction in lowest form of the following–

(i) 18%

Ans: 18%

= 18/100

= 18

Again, 18/100

= 9/50

(ii) 0.25%

Ans: 0.25%

= 25/100 × 100

= 25/10000

= 0.0025

Again, 25/100 × 100

= 1/400

(iii) 60%

Ans: 60%

= 60/100

= 0.60

Again, 60/100

= 3/5

(iv) 42.5%

Ans: 42.5%

= 425/10 × 100

= 0.425

Again, 425/10 × 100

= 17/40

(v) 56%

Ans: 56%

= 56/100

= 0.56

Again, 56/100 = 14/25

5. Express in percentage–

(i) 4:10

Ans: 4:10

= 4/10 × 100%

= 40%

(ii) 11:20

Ans: 11:20

= 11/20 × 100%

= 55%

(iii) 19:50

Ans: 19:50

= 19/50 × 100%

= 38%

(iv) 3:25

Ans: 3:25

= 3/25 × 100%

= 12%

(v) 9:4

Ans: 9:4

= 9/4 × 100%

= 225%

6. Express in ratio–

(i) 72%

Ans: 72%

= 72/100

= 18/25

= 18:25

(ii) 15/4%

Ans: 15/4%

= 15/4 × 100

= 3/80

= 3:80

(iii) 0.14%

Ans: 0.14%

= 14/100 × 100

= 7/5000

= 7:5000

(iv) 6 2/5%

Ans: 6 2/5%

= 32/5 × 100

= 8/125

= 8:125

(v) 4.6%

Ans: 4.6%

= 46/10 × 100

= 23/500

= 23:500

7. Express the coloured portion of the following figures in percentage–

(i)

Ans: = 1/4 × 100%

= 25%

Ans: = ½/3 × 100%

= 1/6 × 100%

= 50/3%

= 16 ⅔%

Ans: 12/40 × 100%

= 30%

8. Express in percentage–

(i) 8 hours of day.

Ans: 8 hours of day

= 8/24 hours

= 1/3 × 100%

= 33 ⅓%

(ii) 72 person out of 80.

Ans: 72 person out of 80

= 72/80 × 100%

= 90%

(iii) 25 paisa of Rs. 5.

Ans: 25 paisa of Rs. 5

= 25/5paisa/Rupees

= 25/5 × 1/100

= 1/20 × 100

= 5%

9. Determine the value–

(i) 20% of 50

Ans: 20% of 50

= 50 × 20/100

= 10

(ii) 30% of Rs 600

Ans: 30% of Rs 600

= Rs. (600 × 30/100)

= Rs. 108

(iii) 20% of 5 km.

Ans: 20% of 5 km

= 5 × 1000 × 20/100 m

= 100 m

= 1 km

(iv) 30% of 1 hours

Ans: 30% of 1 hours

= 60 × 30/100 minutes

= 18 minutes.

10. If value of 20% of a number is 50, determine the number.

Ans: Let the number be x

A/Q, 20% of x = 50

⇒ 20 × x/100 = 50

⇒ x = 250.

∴ The reqd. Number = 250.

11. 13% of which number is 91?

Ans: Let the number be x

A/Q, 13% of x = 91

⇒ 13x/100 = 91

⇒ 13x = 91 × 100

⇒ x = 91 × 100/13 = 700

∴ The reqd. Number is 700.

12. What percentage of 40 is 16?

Ans: Let the percentage be x%

∴ x% of 40 = 16

⇒ 400 × x/100 = 16

⇒ 2x/5 = 16

⇒ 2x = 16 × 5/2 = 40%

∴ The reqd. Number is 40%

13. Express ’30 out of 40′ and ’40 out of 50′, both in percentage. Which is greater?

Ans:

∴ 40 out of 50 is greater than 30 out of 40.

14. The area of a garden is 400 square meter. The garden is arranged in the following manner.

(i) 30% space of the garden is reserved for flowers. Find the area of the space for flowers.

Ans: The area of garden = 400 sq. m.

30% space of the garden is reserved for flowers.

∴ Area of the space for flowers

= 30% of 400 sq.m.

= 30 × 400/100 sq. m.

= 120 sq.m.

(ii) The area of a pond in the garden is 80 square meter. What percentage of the garden is covered by the pond?

Ans: The area of pond in the garden is 80 sq.m.

∴ The reqd. percentage = 80/400 × 100

= 20%

Exercise – 8.3

1. Find the profit or loss in the following transactions. Also find profit percent or loss percent in each case.

(a) A ball bought for Rs. 300 and sold for Rs. 450.

Ans: Profit = Selling price – Cost price

= Rs. (450 – 300)

= Rs. 150

∴ Profit percentage = Profit/Cost Price × 100%

= 150/300 × 100%

= 50%

Ans. Profit = Rs. 150 and Profit percentage 50%

(b) A TV bought for 10,000 and sold for Rs. 15,500.

Ans: Profit = Selling price – Cost price

= Rs. (15,500 – 10,000)

= Rs. 5,500, Profit percent = 50%

∴ Profit percent = 5,500/10,000 × 100%

= 55%

Ans. Profit = Rs. 5,500, Profit percent = 55%

(c) A cupboard bought for Rs. 5,000 and sold for Rs. 3,500.

Ans: Loss = Rs. (5,000 – 3500)

= Rs. 1500

∴ Loss percent = 1500/5000 × 100%

= 30%

Ans. Loss = Rs. 1500 and Loss percent = 30%

(d) A shirt bought for Rs. 400 and sold for Rs. 280.

Ans: Loss = Rs. (400 – 280)

= Rs. 120

∴ Loss percent = 120/400 × 100%

= 30%

Ans. Loss = Rs. 120, Loss percent = 30%

2. Population of an area decreases from 45,000 to 42,000. Calculate percentage of decrease.

Ans: Population of an area from 45,000 to 42,000

∴ Decreases population = 45,000 – 42,000

= 3,000

∴ Percentage of decrease = 3,000/45,000 × 100%

= 20/3%

= 6 ⅔%

3. A book bought for Rs. 250 and sold for Rs. 190. What is the profit or loss in percentage?

Ans: Loss = Rs. (250 – 190)

= Rs. 60

∴ Loss percentage = 60/250 × 100

= 24%

4. Rohan has bought a TV for Rs. 10,500 and sold if at a profit of 30% Calculate the selling price of the TV.

Ans: Let,

The cost price = Rs. 100

∴ Selling price = Rs. (100 + 30)

= Rs. 130

∴ If C. P. is Rs. 100

S.P. = Rs. 130

∴ If C.P. is Rs.1 S.P. = Rs. 130/100

∴ If C.P. is Rs. 10,500 S.P. = Rs. 130/100 × 10500

= 13,650

Ans. Selling price of the TV = Rs. 13,650

5. Sumona has bought a car for Rs. 2,50,000 and sold for Rs. 2,30,000. What is the loss or profit in percentage?

Ans: Loss = Rs. (2,50,000 – 2,30,000)

= 20,000

∴ Loss percentage = 20000/250000 × 100%

= 8%

6. A motor cycle has been sold for Rs. 23,000 at a profit of 15%. What is the cost price of the motor cycle?

Ans: Let, C. P. = Rs. 100

∴ S.P. = Rs. (100 + 15)

= Rs. 115

∴ If S.P. is Rs. 115, C.P. = 100

∴ If S.P. is Rs. 1, C.P. = Rs. 100/115

∴ If S.P. is Rs. 23,000 C.P.

= Rs.100 × 23,000/115

= 20,000

∴ Cost price = 20,000

7. Ratan has bought an almirah for Rs. 6,250 and sold at a loss of 24%. What is the selling price of the almirah?

Ans: Let the C.P. = Rs. 100

Now, S.P. = Rs. (100 – 24)

= Rs. 76

∴ Selling price = 76 × 6250/100

= Rs. (38 × 125)

= Rs. 4750

8. Determine the interest of Rs. 5000 at 8% rate of interest per annum for 3 years.

Ans: Here, P = Rs. 5000

Rate of interest (R) = 8,

Time (T) = 3 years

∴ The reqd. S.I. = P × R × T/100

= Rs. 5000 × 8 × 3/100

= (50 × 24)

= Rs. 1200

9. Dalimi pays Rs. 120 as interest for one year at a rate of interest of 5%. How much money did she borrow?

Ans: Rs. 5 as the interest on Rs. 100

∴ Rs. 1 as the interest on Rs. 100/5

∴ Rs. 120 as the interest on Rs. 100 × 120/5

= Rs. 2400

Ans. She borrowed = Rs. 2400.

10. Find out the interest of Rs. 1,25,000 at 10% rate of interest for a period of 1 year and 6 months.

Ans: Let, the principal (P) = Rs. 1,25,000

Rate of interest ( R) = 10%

And time (T) = 1 year and 6 months

= 1 6/12 years

= 3/2 years

∴ Interest (I) = P × R × T/100

= 1,25,000 × 10 × 3/100 × 2

= Rs. (6250 × 3)

= Rs. 18,750

11. Find out the interest and total amount of Rs. 1500 at rate of interest of Rs. 12 per annum for 2 years and 9 months.

Ans: Principal (P) = Rs. 1500

Rate of interest (R) = 12

Time (T) = 2 years and 9 months

= 2 9/12 years

= 11/4 years

∴ Interest = P × R × T/100

= Rs. 1500 × 12 × 11/100 × 4

= Rs.15 × 3 × 11

= Rs. 495

Now, interest = Rs. 495

And Amount = I + P

= Rs. (495 + 1500)

= Rs. 1995