CG Board Class 9 Mathematics Chapter 7 Solutions: Comparing Quantity (राशियों की तुलना) – 2026-27

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CG SCERT (Chhattisgarh Board) Class 9 Mathematics Solutions | 2026-27 Official Edition

Complete 100% textbook-grounded CG Board Class 9 Mathematics Chapter 7 Solutions: Comparing Quantity (राशियों की तुलना) in Bilingual Format (English & Hindi Medium).

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Q1

Give five examples from your daily experience where…


📝 Question:

Give five examples from your daily experience where you find definite ratio or proportion between different quantities

💡 Solution:

  1. Map Scales: 1 cm on a map represents a fixed distance (e.g., 10 km) in reality.
  2. Recipes: Mixing 1 cup of urad dal with 2 cups of rice to make batter (ratio 1 : 2).
  3. Speed and Distance: Traveling at a constant speed gives a constant ratio of distance to time.
  4. Model Scaling: Ratio of dimensions of a toy car to an actual car.
  5. Financial Shares: Profit sharing in a partnership business based on invested capital ratios.

Q2

Consider the following examples carefully and discuss which…


📝 Question:

Consider the following examples carefully and discuss which way of comparison, ratio or percentages would be better? 1. The mixture for Idli contains 1/3 urad lentil (33.3\% urad lentil) and 2/3 rice (66.6\% rice). 2. The distribution of children in the class is Girls : Boys = 3 : 2 (60\% Girls, 40\% Boys)

💡 Solution:

  1. For Idli mixture: Ratio (1/3 : 2/3 or 1 : 2) is better because while cooking, measuring parts/cups directly is more practical than calculating percentages.
  2. For Class Distribution: Percentage (60\% Girls, 40\% Boys) is better because it gives an immediate picture of relative strength regardless of total class size.

Q3

Try This Page 131132 Q1 Whenever you go…


📝 Question:

Try This (Page 131-132) / * Q.1 Whenever you go shopping with your family, look at the bill and see the products on which sales tax is charged. Make a list

💡 Solution:

  • List of taxable items: Soap, Toothpaste, Clothes, Electronics, Packaged Food items.

(i) Take a discount of 10\% and add 5\% sales tax.

(ii) Add 5\% sales tax and then take 10\% discount.

  • Solution / :
  • Let Marked Price (MP) = Rs. 100
  • Case (i):
  • Price after 10\% discount = 100 – 10 = Rs. 90
  • Sales tax of 5\% on Rs. 90 = 90 × 5/100 = Rs. 4.50
  • Final Price = 90 + 4.50 = Rs. 94.50
  • Case (ii):
  • Price after 5\% sales tax = 100 + 5 = Rs. 105
  • Discount of 10\% on Rs. 105 = 105 × 10/100 = Rs. 10.50
  • Final Price = 105 – 10.50 = Rs. 94.50
  • Conclusion: Both options result in the exact same final payable amount (Rs. 94.50).
Q4

Try This Page 138 Q1 Find compound interest…


📝 Question:

Try This (Page 138) / * Q.1 Find compound interest after 2 years on Rs. 15,000 at 6\% annual rate

💡 Solution:

  • P = 15000, R = 6\%, t = 2 years
  • A = P (1 + R/100)t = 15000 (1 + 6/100)2 = 15000 × (53/50)2 = 15000 × (2809)/(2500) = Rs. 16,854
  • C.I. = A – P = 16854 – 15000 = Rs. 1,854

  • Solution / :
  • P = 8000, R = 5.5\% = 11/2\%, t = 3 years
  • A = 8000 (1 + 11/200)3 = 8000 × (211/200)3 = 8000 × (9393931)/(8000000) = Rs. 9,393.93
  • C.I. = 9393.93 – 8000 = Rs. 1,393.93

(i) On Rs. 10,700 after 3 years at 141/2\% per annum.

(ii) On Rs. 18,000 after 2 years at 10\% per annum.

  • Solution / :
  • (i) P = 10700, R = 14.5\%, t = 3 years
  • A = 10700 (1 + (14.5)/(100))3 = 10700 × (1.145)3 = Rs. 16,061.85
  • C.I. = 16061.85 – 10700 = Rs. 5,361.85
  • (ii) P = 18000, R = 10\%, t = 2 years
  • A = 18000 (1 + 10/100)2 = 18000 × 121/100 = Rs. 21,780
  • C.I. = 21780 – 18000 = Rs. 3,780
Q5

Try This Page 139 Q1 Calculate compound interest…


📝 Question:

Try This (Page 139) / * Q.1 Calculate compound interest for 11/2 years on Rs. 4,000 at 5\% rate of interest

💡 Solution:

  • For 1 full year: A1 = 4000 (1 + 5/100) = Rs. 4,200
  • Simple interest for remaining 1/2 year on Rs. 4200 = (4200 × 5 × 1)/(2 × 100) = Rs. 105
  • Total Amount A = 4200 + 105 = Rs. 4,305
  • C.I. = 4305 – 4000 = Rs. 305

  • Solution / :
  • P = 1500, Half-yearly rate R = 10/2 = 5\%, Time t = 1.5 × 2 = 3 half years
  • A = 1500 (1 + 5/100)3 = 1500 × (21/20)3 = 1500 × (9261)/(8000) = Rs. 1,736.44
  • C.I. = 1736.44 – 1500 = Rs. 236.44

(i) Interest is compounded annually.

(ii) Interest is compounded half yearly.

  • Solution / :
  • (i) Annually:
  • A = 80000 (1 + 10/100)2 = 80000 × 121/100 = Rs. 96,800
  • (ii) Half-yearly:
  • Rate = 5\%, t = 4 half years
  • A = 80000 (1 + 5/100)4 = 80000 × (21/20)4 = 80000 × (194481)/(160000) = Rs. 97,240.50
Q6

Try This Page 145 Q1 Present population of…


📝 Question:

Try This (Page 145) / * Q.1 Present population of a village is 8000. If decreasing at 5\% annually, find population after 3 years

💡 Solution:

  • Expected Population = 8000 (1 – 5/100)3 = 8000 × (19/20)3 = 8000 × (6859)/(8000) = 6,859

  • Solution / :
  • Expected Population = 9600 (1 + 15/100)2 = 9600 × (23/20)2 = 9600 × 529/400 = 24 × 529 = 12,696
  • Solution / :
  • Let monthly salary = Rs. x
  • Saving percentage = 100\% – 75\% = 25\%
  • 25\% of x = 3950 ⇒ 25/100 × x = 3950 ⇒ x = 3950 × 4 = Rs. 15,800
  • Solution / :
  • Let total students = N
  • 60\% of N = 18 ⇒ 60/100 N = 18 ⇒ N = 30
  • Number of girls = 18; Number of boys = 30 – 18 = 12
  • Ratio of Boys : Girls = 12 : 18 = 2 : 3
  • Solution / :
  • Discount = Marked Price – Selling Price = 950 – 760 = Rs. 190
  • Discount Percent = 190/950 × 100 = 20\%
  • Solution / :
  • Let original price = Rs. P
  • P × (1 + 12/100) = 9016 ⇒ P × 112/100 = 9016 ⇒ P = (9016 × 100)/(112) = Rs. 8,050
  • Solution / :
  • Sales Tax = 130000 × 7/100 = Rs. 9,100
  • Total Paid = 130000 + 9100 = Rs. 1,39,100
  • Solution / :
  • Let Marked Price = Rs. M
  • M × (1 – 8/100) = 1748 ⇒ M × 92/100 = 1748 ⇒ M = (1748 × 100)/(92) = Rs. 1,900
  • Solution / :
  • Basket 1 Ratio (Mangoes : Watermelons) = 8 : 4 = 2 : 1
  • Basket 2 Ratio (Mangoes : Watermelons) = 14 : 7 = 2 : 1
  • Conclusion: Ratios in both baskets are *Equal.

(i) Shirt priced at Rs. 200.

(ii) 5 kg sugar at Rs. 30 per kg.

  • Solution / :
  • (i) Price = 200; Tax = 200 × 5/100 = 10 ⇒ SP = 200 + 10 = Rs. 210
  • (ii) Price = 5 × 30 = 150; Tax = 150 × 5/100 = 7.50 ⇒ SP = 150 + 7.50 = Rs. 157.50
  • Solution / :
  • Let Price = P
  • P × 115/100 = 5750 ⇒ P = (5750 × 100)/(115) = Rs. 5,000
  • Solution / :
  • Let Price = P
  • P × 108/100 = 10260 ⇒ P = (10260 × 100)/(108) = Rs. 9,500

(i) P = 7000, R = 10\%, t = 4 years.

(ii) P = 6250, R = 12\%, t = 2 years.

(iii) P = 16000, R = 5\%, t = 3 years.

  • Solution / :
  • (i) A = 7000 (1 + 10/100)4 = 7000 × 1.4641 = Rs. 10,248.70; C.I. = 10248.70 – 7000 = Rs. 3,248.70
  • (ii) A = 6250 (1 + 12/100)2 = 6250 × (28/25)2 = Rs. 7,840; C.I. = 7840 – 6250 = Rs. 1,590
  • (iii) A = 16000 (1 + 5/100)3 = 16000 × (21/20)3 = Rs. 18,522; C.I. = 18522 – 16000 = Rs. 2,522
  • Solution / :
  • A = 125000 (1 + 12/100)3 = 125000 × (28/25)3 = 125000 × (21952)/(15625) = Rs. 1,75,616
  • C.I. = 175616 – 125000 = Rs. 50,616
  • Solution / :
  • A = 50000 (1 + 15/100)2 = 50000 × (23/20)2 = 50000 × 529/400 = Rs. 66,125
  • C.I. = 66125 – 50000 = Rs. 16,125
  • Solution / :
  • S.I. = (1260 × 5 × 2)/(100) = Rs. 126
  • A = 1260 (1 + 5/100)2 = 1260 × 441/400 = Rs. 1389.15 ⇒ C.I. = Rs. 129.15
  • Difference = 129.15 – 126 = Rs. 3.15
  • Solution / :
  • S.I. = (8000 × 10 × 2)/(100) = Rs. 1600
  • C.I. = 8000 [(1 + 10/100)2 – 1] = 8000 × 21/100 = Rs. 1680
  • Difference = 1680 – 1600 = Rs. 80
  • Solution / :
  • Half-yearly Rate R = 4\%, t = 3 half years
  • A = 3000 (1 + 4/100)3 = 3000 × (26/25)3 = 3000 × (17576)/(15625) = Rs. 3374.592
  • C.I. = 3374.592 – 3000 = Rs. 374.59
  • Solution / :
  • Quarterly Rate = 8/4 = 2\%, Time t = 4 quarters
  • A = 9000 (1 + 2/100)4 = 9000 × (1.02)4 = 9000 × 1.08243216 = Rs. 9741.89
  • C.I. = 9741.89 – 9000 = Rs. 741.90
  • Solution / :
  • Half-yearly Rate = 6\%, t = 2 half years
  • A = 3500 (1 + 6/100)2 = 3500 × (2809)/(2500) = Rs. 4044.60 ⇒ C.I. = Rs. 544.60 or 544.69
  • Solution / :
  • Half-yearly Rate = 10\%, t = 2 half years
  • A = 25000 (1 + 10/100)2 = 25000 × 121/100 = Rs. 30,250
  • Solution / :
  • Quarterly Rate = 3\%, Time = 6 months = 2 quarters
  • A = 10000 (1 + 3/100)2 = 10000 × (10609)/(10000) = Rs. 10,609
  • C.I. = 10609 – 10000 = Rs. 609
  • Solution / :
  • 6615 = P (1 + 5/100)2 = P × 441/400 ⇒ P = (6615 × 400)/(441) = Rs. 6,000
  • Solution / :
  • Rate = 5\%, t = 3 half years
  • 18522 = P (1 + 5/100)3 = P × (9261)/(8000) ⇒ P = (18522 × 8000)/(9261) = Rs. 16,000
  • Solution / :
  • 17576 = 15625 (1 + R/100)3 ⇒ (17576)/(15625) = (1 + R/100)3
  • (26/25)3 = (1 + R/100)3 ⇒ 1 + R/100 = 26/25 ⇒ R/100 = 1/25 ⇒ R = 4\%
  • Solution / :
  • (6615)/(6000) = (1 + R/100)2 ⇒ 441/400 = (1 + R/100)2 ⇒ (21/20)2 = (1 + R/100)2 ⇒ R = 5\%
  • Solution / :
  • (9261)/(8000) = (1 + 5/100)t ⇒ (21/20)3 = (21/20)t ⇒ t = 3 years
  • Solution / :
  • Total Amount A = 46875 + 5853 = Rs. 52,728
  • Rate = 4\%, (52728)/(46875) = (1 + 4/100)n ⇒ (17576)/(15625) = (26/25)n ⇒ n = 3 half years = 11/2 years
  • Solution / :
  • Difference = P (R/100)2 ⇒ 40 = P (5/100)2 ⇒ 40 = P × 1/400 ⇒ P = Rs. 16,000
  • Solution / :
  • Balance Principal = 450 – 210 = Rs. 240
  • Total paid in instalments = 2 × 125 = Rs. 250
  • Total interest paid = 250 – 240 = Rs. 10
  • Principal for 1st month = 240; Principal for 2nd month = 240 – 125 = 115
  • Total Principal for 1 month = 240 + 115 = Rs. 355
  • 10 = (355 × R × 1)/(100 × 12) ⇒ R = (12000)/(355) = 33.80\% or 33.8\%
  • Solution / :
  • Balance = 3000 – 600 = 2400
  • Total paid = 2500 ⇒ Interest = Rs. 100
  • Total Principal for 1 month = 2400 + (2400 – 1250) = 2400 + 1150 = Rs. 3550
  • 100 = (3550 × R × 1)/(1200) ⇒ R = (120000)/(3550) = 33.8\%
  • Solution / :
  • Balance payable = 1940 – 620 = Rs. 1,320
  • Let each instalment = Rs. x
  • Solving monthly instalment formula: Each instalment = Rs. 673.11
  • Solution / :
  • Balance = 20100 – 3700 = Rs. 16,400
  • Let each instalment = Rs. x
  • Solving monthly instalment formula: Each instalment = Rs. 8,302.075
  • Solution / :
  • Total instalment paid = 440
  • Let Cash Price = P ⇒ Present worth calculation gives Cash Price = Rs. 639.35
  • Solution / :
  • Remaining Balance = 20000 – 11000 = Rs. 9,000
  • Let each annual instalment = x
  • P1 + P2 = 9000 ⇒ x (100/125) + x (100/125)2 = 9000 ⇒ 4/5x + 16/25x = 9000 ⇒ 36/25x = 9000 ⇒ x = Rs. 6,250
  • Solution / :
  • Balance = 12000 – 3600 = Rs. 8,400, Half-yearly Rate = 10\%
  • x (10/11) + x (10/11)2 = 8400 ⇒ 210/121x = 8400 ⇒ x = Rs. 4,840
  • Solution / :
  • Balance = 3000 – 450 = Rs. 2,550, Half-yearly Rate = 2\%
  • x (50/51) + x (50/51)2 = 2550 ⇒ x × (50 × 101)/(2601) = 2550 ⇒ x = Rs. 1,313.30

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