Set B Solutions

B1. Let CP = 100. MP = 150. After 20% discount: 150×0.8 = 120. After 10% discount: 120×0.9 = 108. Profit = 108−100 = 8. Answer: (b) 8% profit (Shortcut used: Trick 1, CP=100)

B2. Take true weight = 1000 g, CP of 1000 g = Rs 1000 (rate Re 1/g). Actual CP of 800 g physically given = Rs 800. SP charged = price of 1000 g marked up 10% = 1000×1.10 = 1100. Profit = 1100−800 = 300. Profit% = (300/800)×100 = 37.5%. Answer: (c) 37.5% (Shortcut used: actual-cost-vs-actual-revenue method for combined markup + false weight, Section 2.6)

B3. Let CP of profit-horse = C₁, loss-horse = C₂. C₁+C₂ = 15000. Net profit = 0 ⇒ 0.20C₁ = 0.10C₂ ⇒ C₂ = 2C₁. So C₁+2C₁=15000 ⇒ C₁ = 5000. Answer: (b) Rs 5000 (Same pattern as Worked Example 25)

B4. Total CP = 30×20 + 20×25 = 600+500 = 1100. Total qty = 50 kg, Total SP = 50×26 = 1300. Profit = 200. Profit% = (200/1100)×100 = 18.18%. Answer: (c) 18.18%

B5. SP = 4000 × 0.9 × 0.8 × 0.75. Step: 0.9×0.8 = 0.72; 0.72×0.75 = 0.54. SP = 4000×0.54 = 2160. Answer: (c) Rs 2160

B6. SP = CP × 1.26 = 900×1.26 = 1134. MP = SP/(1−0.10) = 1134/0.9 = 1260. Answer: (c) Rs 1260

B7. CP of 45 lemons: SP=40 at 20% loss ⇒ CP = 40×100/80 = 50. CP per lemon = 50/45 = 10/9. To gain 20%, SP per lemon = (10/9)×1.2 = 12/9 = 4/3. Number of lemons for Rs 24 = 24 ÷ (4/3) = 24×3/4 = 18. Answer: (c) 18

B8. By shortcut, Loss% = 10²/100 = 1%. CP₁ = 1980/1.1 = 1800; CP₂ = 1980/0.9 = 2200; total CP = 4000; total SP = 3960; Loss = 4000−3960 = Rs 40. Answer: (c) Rs 40 (Shortcut used: Trick 8, same-SP-equal-% ⇒ loss% = x²/100)

B9. Let CP = x. MP = 1.4x. After 10% discount: 1.4x×0.9 = 1.26x. After 20% discount: 1.26x×0.8 = 1.008x. SP−CP = 1.008x − x = 0.008x = 50.40 ⇒ x = 50.40/0.008 = 6300. Answer: (c) Rs 6300

B10. Error = 1000−750 = 250; base = 750. Gain% = (250/750)×100 = 33.33%. Answer: (c) 33.33%

B11. Let CP=100. MP=125. SP after 12% discount = 125×0.88 = 110. Gain% = 10%. Answer: (b) 10%

B12. Let MP=100. Overall discount 32% ⇒ SP=68. After first discount 20%: 100×0.8=80. Let second discount=d%: 80×(1−d/100)=68 ⇒ 1−d/100=0.85 ⇒ d=15%. Answer: (b) 15%

B13. Let CP = x. SP₁ (8% loss) = 0.92x. SP₂ (10% gain) = 1.10x. Difference = 1.10x − 0.92x = 0.18x = 198 ⇒ x = 198/0.18 = 1100. Answer: (c) Rs 1100

B14. Total CP = 200×12 = 2400. SP of 150 = 150×12×1.20 = 2160. SP of 50 = 50×12×0.95 = 570. Total SP = 2160+570 = 2730. Profit = 2730−2400 = 330. Profit% = (330/2400)×100 = 13.75%. Answer: (b) 13.75% (Shortcut check via Trick 12: (150×20 − 50×5)/200 = (3000−250)/200 = 13.75, confirms the answer instantly)

B15. SP = CP×1.20 = 640×1.20 = 768. MP = SP/(1−0.20) = 768/0.8 = 960. Answer: (d) Rs 960

B16. Let CP = x. SP₁ (12% profit) = 1.12x. SP₂ (20% profit) = 1.20x. Difference = 1.20x − 1.12x = 0.08x = 108 ⇒ x = 108/0.08 = 1350. Check: SP₁ = 1350×1.12 = 1512; SP₂ = 1350×1.20 = 1620; difference = 108 ✓. Answer: (d) Rs 1350 (Shortcut used: Trick 9, CP = a×100/(p₂−p₁) = 108×100/8 = 1350)

B17. MP × 0.75 × 0.85 = 2040 ⇒ MP × 0.6375 = 2040 ⇒ MP = 2040/0.6375 = 3200. Check: 3200×0.75 = 2400; 2400×0.85 = 2040 ✓. Answer: (c) Rs 3200

B18. Using Profit% = [(1000−w)/w]×100: 60 = [(1000−w)/w]×100 ⇒ 60w = 100000 − 100w ⇒ 160w = 100000 ⇒ w = 625. Answer: (b) 625 g

B19. A’s equivalent capital: first 6 months at 12000, next 6 months at 12000+6000=18000. A = 12000×6 + 18000×6 = 72000+108000 = 180000. B’s equivalent capital = 16000×12 = 192000. Ratio A:B = 180000:192000 = 15:16 (dividing by 12000). Sum = 31. Each part = 6200/31 = 200. B’s share = 16×200 = 3200. Answer: (d) Rs 3200

B20. Overall% = 0 ⇒ (30m − 15n)/(m+n) = 0 ⇒ 30m = 15n ⇒ m/n = 15/30 = 1:2. Answer: (a) 1:2

B21. Let CP = 100. MP = 160. SP after 20% discount = 160×0.8 = 128. Gain = 128−100 = 28. Answer: (c) 28%

B22. True weight = 1000 g, CP = 1000. Actual cost of 800 g given = 800. SP charged = price of claimed 1000 g at 6% loss = 1000×0.94 = 940. Profit = 940−800 = 140. Profit% = (140/800)×100 = 17.5%. Answer: (c) 17.5% profit

B23. Let CP = 100. MP = 180. After 25% discount: 180×0.75 = 135. After 10% discount: 135×0.9 = 121.5. Profit = 21.5%. Answer: (c) 21.5% profit

B24. Let CP of profit-bicycle = C₁, loss-bicycle = C₂. C₁+C₂ = 7000. Net profit = 0 ⇒ 0.15C₁ = 0.20C₂ ⇒ C₁ = (4/3)C₂. So (4/3)C₂+C₂ = 7000 ⇒ (7/3)C₂ = 7000 ⇒ C₂ = 3000. Check: C₁ = 4000; profit on C₁ = 0.15×4000 = 600; loss on C₂ = 0.20×3000 = 600 — equal, net zero ✓. Answer: (b) Rs 3000

B25. Total CP = 20×18 + 30×22 + 10×30 = 360+660+300 = 1320. Total qty = 60 kg. Total SP = 60×25 = 1500. Profit = 180. Profit% = (180/1320)×100 = 13.64% (150/11%). Answer: (b) 13.64%

B26. SP = 5000 × 0.9 × 0.8 × 0.9. Step: 0.9×0.8 = 0.72; 0.72×0.9 = 0.648. SP = 5000×0.648 = 3240. (Equivalent single discount = 35.2%.) Answer: (c) Rs 3240

B27. CP of 20 oranges: SP=80 at 20% loss ⇒ CP = 80×100/80 = 100. CP per orange = 100/20 = 5. To gain 25%, SP per orange = 5×1.25 = 6.25. Number of oranges for Rs 75 = 75/6.25 = 12. Answer: (b) 12

B28. SP = CP×1.19 = 1700×1.19 = 2023. MP = SP/(1−0.15) = 2023/0.85 = 2380. Answer: (c) Rs 2380

B29. A’s equivalent capital: months 0–4 at 20000, months 4–12 (8 months) at 20000−5000=15000. A = 20000×4 + 15000×8 = 80000+120000 = 200000. B’s equivalent capital = 25000×12 = 300000 (unchanged all year). C’s equivalent capital: months 0–6 at 30000, months 6–12 (6 months) at 30000+10000=40000. C = 30000×6 + 40000×6 = 180000+240000 = 420000. Ratio A:B:C = 200000:300000:420000 = 10:15:21 (dividing by 20000). Sum = 46. Each part = 23000/46 = 500. B’s share = 15×500 = 7500. Answer: (c) Rs 7500

B30. True weight = 1000 g, CP = 1000. Actual cost of 950 g given = 950. MP = 1000×1.30 = 1300. SP after successive discounts of 20% and 5% = 1300×0.80×0.95 = 1300×0.76 = 988. Profit = 988−950 = 38. Profit% = (38/950)×100 = 4%. Answer: (b) 4%