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).
Official Textbook Exercises
End-of-Chapter Exercises (Solutions)
अभ्यास के सभी प्रश्नों के हल
Question 1
Exercise Question
प्रश्न 1: मोहन अपने वेतन का 75\% खर्च करने के बाद Rs. 3,950 …
📝 Question:
(i) Shirt priced at Rs. 200.
(ii) 5 kg sugar at Rs. 30 per kg.
(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:
- 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.
- 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
- 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